Vitruvius, De architectura libri decem, 1567

Table of figures

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[91] A. Templum diui Marci.B. Turris diui Marci.C. Duæ columne.D. Forum diui ’Marci.E. D. Geminianus.F. D. Moyſes.G. D. Baſſus.H. D. Theodorus.I. D. Zacharias.K. D. Ioan. embracora.L. D. Martinus.M. D. Dominicus.N. D. Antonius.O. D. Petrus.P. D. Daniel.Q. D. Donatus.R. Dogana.S. Nauale.T. D. Cœleſtis.V. D. Franciſcus.X. D. Io. & Paulus.Y. D. Laurentius.Z. D. Seuerus.a. D. Marina.b. D. Cantianus.c. D. Apoſtoli.d. Crucigeri.e. D. Sophia.f. D. Maria ab hortis.g. D. Iob.h. S. Crux.i. D. Margarita.k. Magna domus Franciſcanorum.l. D. Paulus.m. D. Auguſtinus.n. D. Agatha.o. D. Maria mater domini.p. D. Caßiani.q. D. Matthia.r. D. Iacobus in riuo alto.ΔΔΔ. Magnus canalis.ſ. Forum riui alti.t. Pons riui alti.@. D. Maria Iubanica.x. D. Stephanus.y. Templum charitatis.Z. D. Gregorius. TRAMONTANAPONENTELEVANTE
[92] B G F M A H I N E C D
[93] A. tetrastylon cauum ædium.F. cellæ F A FF A F
[94] B. Tuſcanicum cauum ædium.E. cellæ.D. interpenſiua. E B E
[95] D D E B E
[96] C. diſpluuiatum.G. cellæ. G C G
[97] G C G
[98] D. cauædium teſtudinatum.M. cellæ.P. lumen. M D MM D P M
[99] O. cauum ædium.P. alæ.Q. uiridaria.T. ueſtibulum.Z. baſilica.r. tablinum. Z Y Q Q O Q Q T
[Figure 100]
[Figure 101]
[102] FRONTE.
[103] A
[104] Græcorum ædes earumq́; partium diſpoſitiones.A. peristylium amplum.E. peristylium primum.C. aditus amplus.D. aditus ab uno ad aliudperiſtylium.E. proſtas ubi eraut duæ antæ.F. G. Antithalamus.H. I. gynæconitides.K. cu-bicuUmdiebria.L. S. oeci,& bibliotecæ,& ubi ſunt pictores.M. R. pinacotbecæ.N. cyzicena triclinia.O. porticus ad ſeptentrionem.P. cellæ hostiariæ.Q. oeci quadrati.T. V. porticus ad triclinia cizcena.X. hypæthra loca.r. oeci magni ubi matres familiarũ cum lanificijs habent ſeſſiones.Z. hoſpitalia.1. thirorium.2. Equilia.3. cubicula.4. meſaulæ & andronæ.5. triclinia quo-tidiana.6. posthalamus.7. thalamus.8. porticus Rhodiaca altior. T QVNMRN8SALKICHXYYFEG76B543O32P21
[105] Pauimentorum genera.Filandri.Anticum.
[106] c d f b c 8
[107] CHOROBATES.2 I 3 2
[108] d 10 10 a d 50 50 50 c 50 ba s d s 7 {1/14} 25 s b ce 8 8 10 84 f hm 5 43 3 4 4 3 3 4 4 5 5 5 53 5 4
[109] Figura ex meſolabio Architæ ad inueniendas medias.c t @ @ q p o n m l k l h g f p e o ξ v M @ k I o h j ε δ r B d s R q P o N M L K I H G F E L x c 6 N ς ε ξ γ B a
[110] Veſtigium meſolabij Architæ.
[111] Orthographia meſolabij Architæ.
[112] Demonſtratio Eratoſtbenis. a g t cb f b d
[113] Instrumentum Eratoſthenis. m a x g n b c n i o l v q p b e f k d
[114] Vſ{us} demonſtratio Eratoſtbenis cum inſtrumento. a h n ek l i o d b 8 m c 4
[115] Inſtrumentum Platonis. f i n o m
[116] cubus. 8 8 64 8 8 8 8 512 8s e
[117] Demonstratio Archita. p l k b o i m b e d af
[118] Demonctration Platonis. d e b c g
[119] Demostratio ter tiæ proprietatis, & aſſumptionis Nicomedis.instrumentum Nicomedis. f h d g b s n m k a
[120] Duplicatio cubi. e a b c d f g
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            <p style="it">
              <s xml:id="echoid-s21058" xml:space="preserve">
                <pb o="278" file="514.01.310" n="310" rhead="LIBER"/>
              cunda proprietaseſt: </s>
              <s xml:id="echoid-s21059" xml:space="preserve">Quod ſi inter regulam a b. </s>
              <s xml:id="echoid-s21060" xml:space="preserve">& </s>
              <s xml:id="echoid-s21061" xml:space="preserve">flexam lineam ducetur linea, illa tandem flexam ſeca-
                <lb/>
              bit. </s>
              <s xml:id="echoid-s21062" xml:space="preserve">Eſto ergo regula a b. </s>
              <s xml:id="echoid-s21063" xml:space="preserve">polus c. </s>
              <s xml:id="echoid-s21064" xml:space="preserve">atque in interuallo d e.</s>
              <s xml:id="echoid-s21065" xml:space="preserve">deſcribatur flexa,quæ conchoides dicitur. </s>
              <s xml:id="echoid-s21066" xml:space="preserve">& </s>
              <s xml:id="echoid-s21067" xml:space="preserve">
                <lb/>
              inter hanc & </s>
              <s xml:id="echoid-s21068" xml:space="preserve">regulam a b. </s>
              <s xml:id="echoid-s21069" xml:space="preserve">ducatur recta f g h. </s>
              <s xml:id="echoid-s21070" xml:space="preserve">dico f g h. </s>
              <s xml:id="echoid-s21071" xml:space="preserve">flexam lineam ſecaturam. </s>
              <s xml:id="echoid-s21072" xml:space="preserve">ſit f g h.
                <lb/>
              </s>
              <s xml:id="echoid-s21073" xml:space="preserve">æque diſtans lineæ a b. </s>
              <s xml:id="echoid-s21074" xml:space="preserve">aut non ſit. </s>
              <s xml:id="echoid-s21075" xml:space="preserve">poſito ergo prius quod ſit & </s>
              <s xml:id="echoid-s21076" xml:space="preserve">fiat, ut ſicut ſe habet d g. </s>
              <s xml:id="echoid-s21077" xml:space="preserve">ad g c. </s>
              <s xml:id="echoid-s21078" xml:space="preserve">ita
                <lb/>
              ſe habeat d e. </s>
              <s xml:id="echoid-s21079" xml:space="preserve">ad alium, puta k. </s>
              <s xml:id="echoid-s21080" xml:space="preserve">& </s>
              <s xml:id="echoid-s21081" xml:space="preserve">constituto centro c. </s>
              <s xml:id="echoid-s21082" xml:space="preserve">interuallo k. </s>
              <s xml:id="echoid-s21083" xml:space="preserve">ſecet circunferentiam deſcriptã
                <lb/>
              in f. </s>
              <s xml:id="echoid-s21084" xml:space="preserve">atque iungatur c f. </s>
              <s xml:id="echoid-s21085" xml:space="preserve">quæ ſecet ab in l. </s>
              <s xml:id="echoid-s21086" xml:space="preserve">erit ergo ut ſicut d g. </s>
              <s xml:id="echoid-s21087" xml:space="preserve">ſe habet ad g c. </s>
              <s xml:id="echoid-s21088" xml:space="preserve">ita ſe habent l
                <lb/>
              f. </s>
              <s xml:id="echoid-s21089" xml:space="preserve">ad f c. </s>
              <s xml:id="echoid-s21090" xml:space="preserve">Sedſicut eſt d g. </s>
              <s xml:id="echoid-s21091" xml:space="preserve">ad g c. </s>
              <s xml:id="echoid-s21092" xml:space="preserve">ita ſe habebat d e. </s>
              <s xml:id="echoid-s21093" xml:space="preserve">ad k. </s>
              <s xml:id="echoid-s21094" xml:space="preserve">ideſt ad c f. </s>
              <s xml:id="echoid-s21095" xml:space="preserve">ergo d e. </s>
              <s xml:id="echoid-s21096" xml:space="preserve">inuenietur
                <lb/>
              æ qualis ipſi l f. </s>
              <s xml:id="echoid-s21097" xml:space="preserve">quod fieri non potest, ita enim pars æqualis toti eſſet, quod manifeſtum fit producta linea
                <lb/>
              c f. </s>
              <s xml:id="echoid-s21098" xml:space="preserve">donec ſecet flexam lineam per e in o. </s>
              <s xml:id="echoid-s21099" xml:space="preserve">quoniam l f o. </s>
              <s xml:id="echoid-s21100" xml:space="preserve">recta æ qualis est ipſi de ex diſſinitione con-
                <lb/>
              choidis. </s>
              <s xml:id="echoid-s21101" xml:space="preserve">Reliquum igitur est, quod recta f g h. </s>
              <s xml:id="echoid-s21102" xml:space="preserve">ſecet flexam lineam modo ad eaſdem partes ducatur. </s>
              <s xml:id="echoid-s21103" xml:space="preserve">Ve-
                <lb/>
                <note position="left" xlink:label="note-514.01.310-01" xlink:href="note-514.01.310-01a" xml:space="preserve">10</note>
              rum æ quediſtet linea illa, quæ inter a b. </s>
              <s xml:id="echoid-s21104" xml:space="preserve">& </s>
              <s xml:id="echoid-s21105" xml:space="preserve">flexam producetur, & </s>
              <s xml:id="echoid-s21106" xml:space="preserve">ſit ea m g n, ducaturq́; </s>
              <s xml:id="echoid-s21107" xml:space="preserve">per g. </s>
              <s xml:id="echoid-s21108" xml:space="preserve">æ que-
                <lb/>
              diſtans f g. </s>
              <s xml:id="echoid-s21109" xml:space="preserve">regulæ a b. </s>
              <s xml:id="echoid-s21110" xml:space="preserve">ergo f g. </s>
              <s xml:id="echoid-s21111" xml:space="preserve">concurret cum flexa, & </s>
              <s xml:id="echoid-s21112" xml:space="preserve">ideo multo magis concurret m n. </s>
              <s xml:id="echoid-s21113" xml:space="preserve">Cum
                <lb/>
              ergo huiuſmodi proprietates organo collectæ fuerint, uſus eius ad propoſitũ oſtẽdendus erit modo terti a proprie
                <lb/>
              tas adducatur, quæ est huiuſmodi. </s>
              <s xml:id="echoid-s21114" xml:space="preserve">Recta a b. </s>
              <s xml:id="echoid-s21115" xml:space="preserve">& </s>
              <s xml:id="echoid-s21116" xml:space="preserve">prima flexa conchoides cum deſcripta illa nunquam con-
                <lb/>
              current, etiam ſi in infinitum protrahantur, hoc facile innoteſcet, ſi ad formam organi attendatur, quoniam in
                <lb/>
              eadem forma, linea media regulæ e f. </s>
              <s xml:id="echoid-s21117" xml:space="preserve">in deſcribenda flexa ſecat ſemper lineam a b. </s>
              <s xml:id="echoid-s21118" xml:space="preserve">in e. </s>
              <s xml:id="echoid-s21119" xml:space="preserve">quo fit ut nota
                <lb/>
              k. </s>
              <s xml:id="echoid-s21120" xml:space="preserve">nunquam perueniet ad ab. </s>
              <s xml:id="echoid-s21121" xml:space="preserve">licet ad eam continenter accedat, per primam prædictam proprietatem.
                <lb/>
              </s>
              <s xml:id="echoid-s21122" xml:space="preserve">Hoc Nicomedis aſſumptum utile es̃t demonſtrationi ſequenti. </s>
              <s xml:id="echoid-s21123" xml:space="preserve">Si angulus fiet ad rectam quæ altera par-
                <lb/>
              te in infinitum tendat, & </s>
              <s xml:id="echoid-s21124" xml:space="preserve">ſi a puncto extra dato ducatur linea, quæ circa eundem angulum ſecet duas
                <lb/>
              rectas, cuius rectæ lineæ particula inter duas, quæ rectum continent datum angulum, equalis ſit da-
                <lb/>
              tæ lineæ quod hoc modo facies. </s>
              <s xml:id="echoid-s21125" xml:space="preserve">Eſto data linea a b. </s>
              <s xml:id="echoid-s21126" xml:space="preserve">ex parte b, infinita, ſupra quam datus an--
                <lb/>
                <note position="left" xlink:label="note-514.01.310-02" xlink:href="note-514.01.310-02a" xml:space="preserve">20</note>
              gulus b a g. </s>
              <s xml:id="echoid-s21127" xml:space="preserve">nota extra ſit c. </s>
              <s xml:id="echoid-s21128" xml:space="preserve">recta autem data ſic d. </s>
              <s xml:id="echoid-s21129" xml:space="preserve">ab c, ad a b. </s>
              <s xml:id="echoid-s21130" xml:space="preserve">ducatur perpendicula-
                <lb/>
              ris c e. </s>
              <s xml:id="echoid-s21131" xml:space="preserve">cui addatur e f. </s>
              <s xml:id="echoid-s21132" xml:space="preserve">æ qualis ipſi d. </s>
              <s xml:id="echoid-s21133" xml:space="preserve">& </s>
              <s xml:id="echoid-s21134" xml:space="preserve">ex organo a polo c. </s>
              <s xml:id="echoid-s21135" xml:space="preserve">& </s>
              <s xml:id="echoid-s21136" xml:space="preserve">interuallo e f, ad regulam a
                <lb/>
              b deſcribatur linea flexa conchoides prima. </s>
              <s xml:id="echoid-s21137" xml:space="preserve">Ergo ex ſecunda proprietate a g, primæ conchoidis produ-
                <lb/>
              cta eoincidet cum conchoidi f g. </s>
              <s xml:id="echoid-s21138" xml:space="preserve">coincidet ergo in g, & </s>
              <s xml:id="echoid-s21139" xml:space="preserve">linea c g, producta, ſecabit a b. </s>
              <s xml:id="echoid-s21140" xml:space="preserve">in h. </s>
              <s xml:id="echoid-s21141" xml:space="preserve">aio li-
                <lb/>
              neam g h. </s>
              <s xml:id="echoid-s21142" xml:space="preserve">eſſe æqualem ipſi d. </s>
              <s xml:id="echoid-s21143" xml:space="preserve">quod inde patet, quoniam ex conchoidis primæ diffinitione, g h, eſt æ-
                <lb/>
              qualis ipſi e f, ſed ex præ ſumpto e f eſt æ qualis ipſi d. </s>
              <s xml:id="echoid-s21144" xml:space="preserve">ergo ex communi ſententia quæ æ qualia tertio,
                <lb/>
              æ qualia inuicem dicuntur, recta g h, eſt æ qualis ipſi d. </s>
              <s xml:id="echoid-s21145" xml:space="preserve">propoſitum ergo habemus. </s>
              <s xml:id="echoid-s21146" xml:space="preserve">Ex Nicomede igitur duæ
                <lb/>
              mediæ comparabiles hoc modo inuenientur. </s>
              <s xml:id="echoid-s21147" xml:space="preserve">Sint duæ rectæ a b, & </s>
              <s xml:id="echoid-s21148" xml:space="preserve">b c, ad angulos rectos poſitæ, inter
                <lb/>
              quas comparabiles duas medias inuenire oporteat: </s>
              <s xml:id="echoid-s21149" xml:space="preserve">perficiatur parallelogrammum a b c d. </s>
              <s xml:id="echoid-s21150" xml:space="preserve">ſecetur utra-
                <lb/>
              que in duas partes, c d, quidem in e. </s>
              <s xml:id="echoid-s21151" xml:space="preserve">d a. </s>
              <s xml:id="echoid-s21152" xml:space="preserve">uero in f. </s>
              <s xml:id="echoid-s21153" xml:space="preserve">coniungaturq́; </s>
              <s xml:id="echoid-s21154" xml:space="preserve">b e, &</s>
              <s xml:id="echoid-s21155" xml:space="preserve">tranſeat uſque ad a d.
                <lb/>
              </s>
              <s xml:id="echoid-s21156" xml:space="preserve">
                <note position="left" xlink:label="note-514.01.310-03" xlink:href="note-514.01.310-03a" xml:space="preserve">30</note>
              productam in punctum g. </s>
              <s xml:id="echoid-s21157" xml:space="preserve">ſed in linea a d. </s>
              <s xml:id="echoid-s21158" xml:space="preserve">cadat ad rectos angulos linea f h. </s>
              <s xml:id="echoid-s21159" xml:space="preserve">& </s>
              <s xml:id="echoid-s21160" xml:space="preserve">producatur a h. </s>
              <s xml:id="echoid-s21161" xml:space="preserve">quæ
                <lb/>
              ſit & </s>
              <s xml:id="echoid-s21162" xml:space="preserve">qualis ipſi c e. </s>
              <s xml:id="echoid-s21163" xml:space="preserve">& </s>
              <s xml:id="echoid-s21164" xml:space="preserve">iungatur g h. </s>
              <s xml:id="echoid-s21165" xml:space="preserve">cui æque diſtet, a i. </s>
              <s xml:id="echoid-s21166" xml:space="preserve">ita ut angulus k a i, ſit æqualis angulo
                <lb/>
              f g h. </s>
              <s xml:id="echoid-s21167" xml:space="preserve">& </s>
              <s xml:id="echoid-s21168" xml:space="preserve">expræcedenti aſſumpto ducatur recta g i k. </s>
              <s xml:id="echoid-s21169" xml:space="preserve">quæ ſecet a i.</s>
              <s xml:id="echoid-s21170" xml:space="preserve">in i. </s>
              <s xml:id="echoid-s21171" xml:space="preserve">& </s>
              <s xml:id="echoid-s21172" xml:space="preserve">d a. </s>
              <s xml:id="echoid-s21173" xml:space="preserve">in parte a. </s>
              <s xml:id="echoid-s21174" xml:space="preserve">pro-
                <lb/>
              ducta ſupra k. </s>
              <s xml:id="echoid-s21175" xml:space="preserve">ita ut. </s>
              <s xml:id="echoid-s21176" xml:space="preserve">i k. </s>
              <s xml:id="echoid-s21177" xml:space="preserve">ſit æqualis ipſi. </s>
              <s xml:id="echoid-s21178" xml:space="preserve">a h. </s>
              <s xml:id="echoid-s21179" xml:space="preserve">& </s>
              <s xml:id="echoid-s21180" xml:space="preserve">iuncta k b, producatur in l, donec cadat in d c.
                <lb/>
              </s>
              <s xml:id="echoid-s21181" xml:space="preserve">productum. </s>
              <s xml:id="echoid-s21182" xml:space="preserve">Dico iam quod ſicut ſe habet a b. </s>
              <s xml:id="echoid-s21183" xml:space="preserve">ad a k. </s>
              <s xml:id="echoid-s21184" xml:space="preserve">ita a k. </s>
              <s xml:id="echoid-s21185" xml:space="preserve">ad l c. </s>
              <s xml:id="echoid-s21186" xml:space="preserve">& </s>
              <s xml:id="echoid-s21187" xml:space="preserve">l c. </s>
              <s xml:id="echoid-s21188" xml:space="preserve">ad c b. </s>
              <s xml:id="echoid-s21189" xml:space="preserve">quoniam
                <lb/>
              c d. </s>
              <s xml:id="echoid-s21190" xml:space="preserve">est in duas partes diuiſa in e. </s>
              <s xml:id="echoid-s21191" xml:space="preserve">& </s>
              <s xml:id="echoid-s21192" xml:space="preserve">huic apponitur k a. </s>
              <s xml:id="echoid-s21193" xml:space="preserve">ergo ex eadem ſexta ſecundi elementorum,
                <lb/>
              quod eſt ſub d k a. </s>
              <s xml:id="echoid-s21194" xml:space="preserve">cum eo, quod fit ex a f æquale est illi, quod fit ex f k. </s>
              <s xml:id="echoid-s21195" xml:space="preserve">Apponatur commune, quod
                <lb/>
              eſtinter f h. </s>
              <s xml:id="echoid-s21196" xml:space="preserve">ergo quod est ſub d k a cum eo, quod fit ex a f & </s>
              <s xml:id="echoid-s21197" xml:space="preserve">ex f h. </s>
              <s xml:id="echoid-s21198" xml:space="preserve">hoc eſt cum eo, quod fit ex
                <lb/>
              a g. </s>
              <s xml:id="echoid-s21199" xml:space="preserve">æquale est illi, quod fit ex k f. </s>
              <s xml:id="echoid-s21200" xml:space="preserve">& </s>
              <s xml:id="echoid-s21201" xml:space="preserve">ex f h. </s>
              <s xml:id="echoid-s21202" xml:space="preserve">ideſt illi, quod fit ex k h. </s>
              <s xml:id="echoid-s21203" xml:space="preserve">& </s>
              <s xml:id="echoid-s21204" xml:space="preserve">quoniam ſicuti ſe habet
                <lb/>
              l c, ad c d. </s>
              <s xml:id="echoid-s21205" xml:space="preserve">ita ſe habet d a. </s>
              <s xml:id="echoid-s21206" xml:space="preserve">ad a k. </s>
              <s xml:id="echoid-s21207" xml:space="preserve">ſed c e. </s>
              <s xml:id="echoid-s21208" xml:space="preserve">eſt dimidium ipſius c d. </s>
              <s xml:id="echoid-s21209" xml:space="preserve">& </s>
              <s xml:id="echoid-s21210" xml:space="preserve">a g. </s>
              <s xml:id="echoid-s21211" xml:space="preserve">est dupla ipſi d a. </s>
              <s xml:id="echoid-s21212" xml:space="preserve">
                <lb/>
                <note position="left" xlink:label="note-514.01.310-04" xlink:href="note-514.01.310-04a" xml:space="preserve">40</note>
              quoniam ex quarta ſexti elementorum ut ſe habet a b. </s>
              <s xml:id="echoid-s21213" xml:space="preserve">ad d e. </s>
              <s xml:id="echoid-s21214" xml:space="preserve">ita ſe habet g a. </s>
              <s xml:id="echoid-s21215" xml:space="preserve">ad a d. </s>
              <s xml:id="echoid-s21216" xml:space="preserve">ex ſuppoſi-
                <lb/>
              tis b a, eſt dupla ipſi d e. </s>
              <s xml:id="echoid-s21217" xml:space="preserve">ergo g a. </s>
              <s xml:id="echoid-s21218" xml:space="preserve">est dupla ipſi a d. </s>
              <s xml:id="echoid-s21219" xml:space="preserve">ſequetur ergo, ut ſicuti l c. </s>
              <s xml:id="echoid-s21220" xml:space="preserve">ſe habet ad c e.
                <lb/>
              </s>
              <s xml:id="echoid-s21221" xml:space="preserve">ita g a. </s>
              <s xml:id="echoid-s21222" xml:space="preserve">ad a k. </s>
              <s xml:id="echoid-s21223" xml:space="preserve">exæquali & </s>
              <s xml:id="echoid-s21224" xml:space="preserve">permutata proportione,ex uigeſima tertia quinti elementorum. </s>
              <s xml:id="echoid-s21225" xml:space="preserve">ſed ut g a. </s>
              <s xml:id="echoid-s21226" xml:space="preserve">
                <lb/>
              ad a k. </s>
              <s xml:id="echoid-s21227" xml:space="preserve">ita h i. </s>
              <s xml:id="echoid-s21228" xml:space="preserve">ad i k. </s>
              <s xml:id="echoid-s21229" xml:space="preserve">exſecunda ſexti elementorum. </s>
              <s xml:id="echoid-s21230" xml:space="preserve">quoniam ex ſubiectis g h. </s>
              <s xml:id="echoid-s21231" xml:space="preserve">& </s>
              <s xml:id="echoid-s21232" xml:space="preserve">a i. </s>
              <s xml:id="echoid-s21233" xml:space="preserve">ſunt æ qui-
                <lb/>
              distantes, & </s>
              <s xml:id="echoid-s21234" xml:space="preserve">ex decima octaua quinti elementorum componendo ſequitur, quod ſicut ſe habet l e ad c e,
                <lb/>
              ita ſe habeat h k. </s>
              <s xml:id="echoid-s21235" xml:space="preserve">ad k i. </s>
              <s xml:id="echoid-s21236" xml:space="preserve">ſed poſita eſt i k. </s>
              <s xml:id="echoid-s21237" xml:space="preserve">æ qualis c e. </s>
              <s xml:id="echoid-s21238" xml:space="preserve">quoniam i k. </s>
              <s xml:id="echoid-s21239" xml:space="preserve">eſt æqualis ipſi a h. </s>
              <s xml:id="echoid-s21240" xml:space="preserve">& </s>
              <s xml:id="echoid-s21241" xml:space="preserve">a h. </s>
              <s xml:id="echoid-s21242" xml:space="preserve">ipſi
                <lb/>
              c e. </s>
              <s xml:id="echoid-s21243" xml:space="preserve">ergo e l. </s>
              <s xml:id="echoid-s21244" xml:space="preserve">eſt æqualis ipſi h k. </s>
              <s xml:id="echoid-s21245" xml:space="preserve">& </s>
              <s xml:id="echoid-s21246" xml:space="preserve">conſequenter æquale est illud, quod fit e x l e, illi quod fit, ex h
                <lb/>
              k. </s>
              <s xml:id="echoid-s21247" xml:space="preserve">& </s>
              <s xml:id="echoid-s21248" xml:space="preserve">quod fit ex l e, æquale eſt illi, quod fit ſub d l c. </s>
              <s xml:id="echoid-s21249" xml:space="preserve">cum eo quod fit ex c e, per ſextam ſecundi ele-
                <lb/>
              mentorum. </s>
              <s xml:id="echoid-s21250" xml:space="preserve">Eiautem quod est ex h k. </s>
              <s xml:id="echoid-s21251" xml:space="preserve">demonſtratum est æquale eſſe id, quod fit ſub d k a. </s>
              <s xml:id="echoid-s21252" xml:space="preserve">cum eo, quod
                <lb/>
              ex a h. </s>
              <s xml:id="echoid-s21253" xml:space="preserve">Quorumid, quod eſt ex c e, æquale eſt ei, quod ex a h. </s>
              <s xml:id="echoid-s21254" xml:space="preserve">Aequalis nanque poſitaes̃t a h. </s>
              <s xml:id="echoid-s21255" xml:space="preserve">ipſi
                <lb/>
                <note position="left" xlink:label="note-514.01.310-05" xlink:href="note-514.01.310-05a" xml:space="preserve">50</note>
              c e. </s>
              <s xml:id="echoid-s21256" xml:space="preserve">Sed ex communi ſententia, ſi ab æqualibus auferantur æqualia, æqualia ſunt reliqua, igitur quod fit ſub
                <lb/>
              d l c, æquale eſt ei, quod fit ſub d k a atuqui per decimam quartam ſexti æqualium, & </s>
              <s xml:id="echoid-s21257" xml:space="preserve">æquiangulorum pa-
                <lb/>
              rallelogrammorum latera mutua ſe proportione conſequuntur. </s>
              <s xml:id="echoid-s21258" xml:space="preserve">ergo ut ipſa l d. </s>
              <s xml:id="echoid-s21259" xml:space="preserve">ad d k. </s>
              <s xml:id="echoid-s21260" xml:space="preserve">& </s>
              <s xml:id="echoid-s21261" xml:space="preserve">k a. </s>
              <s xml:id="echoid-s21262" xml:space="preserve">ad c l.
                <lb/>
              </s>
              <s xml:id="echoid-s21263" xml:space="preserve">verũ ut d l. </s>
              <s xml:id="echoid-s21264" xml:space="preserve">ad d k. </s>
              <s xml:id="echoid-s21265" xml:space="preserve">et a b ad a k & </s>
              <s xml:id="echoid-s21266" xml:space="preserve">l c. </s>
              <s xml:id="echoid-s21267" xml:space="preserve">ad c b. </s>
              <s xml:id="echoid-s21268" xml:space="preserve">& </s>
              <s xml:id="echoid-s21269" xml:space="preserve">l c. </s>
              <s xml:id="echoid-s21270" xml:space="preserve">ad c b. </s>
              <s xml:id="echoid-s21271" xml:space="preserve">& </s>
              <s xml:id="echoid-s21272" xml:space="preserve">a b, ad a k. </s>
              <s xml:id="echoid-s21273" xml:space="preserve">& </s>
              <s xml:id="echoid-s21274" xml:space="preserve">a k. </s>
              <s xml:id="echoid-s21275" xml:space="preserve">ad a k. </s>
              <s xml:id="echoid-s21276" xml:space="preserve">ad l c.</s>
              <s xml:id="echoid-s21277" xml:space="preserve">& </s>
              <s xml:id="echoid-s21278" xml:space="preserve">ipſa l c, ad c b. </s>
              <s xml:id="echoid-s21279" xml:space="preserve">
                <lb/>
              Duabus igitur datis rectis lineis a b. </s>
              <s xml:id="echoid-s21280" xml:space="preserve">& </s>
              <s xml:id="echoid-s21281" xml:space="preserve">b c. </s>
              <s xml:id="echoid-s21282" xml:space="preserve">mediæ duæ inuentæ ſunt comparabiles, & </s>
              <s xml:id="echoid-s21283" xml:space="preserve">reſpondentes a k. </s>
              <s xml:id="echoid-s21284" xml:space="preserve">
                <lb/>
              & </s>
              <s xml:id="echoid-s21285" xml:space="preserve">l c. </s>
              <s xml:id="echoid-s21286" xml:space="preserve">quod facere propoſitum fuit. </s>
              <s xml:id="echoid-s21287" xml:space="preserve">Cæ terum modi alij ſunt antiquor um inueniendi duas medias compara-
                <lb/>
              biles, quos ne moleſtus ſim, omittam, præſertim cum eos in commentarijs Archimedis uidere poſſis, & </s>
              <s xml:id="echoid-s21288" xml:space="preserve">a Ver
                <lb/>
              Hero diligenter explicati ſint. </s>
              <s xml:id="echoid-s21289" xml:space="preserve">nam Philoponus, Dion Bizantius, Diocles, Pappus in mechanicis, Porus, & </s>
              <s xml:id="echoid-s21290" xml:space="preserve">
                <lb/>
              Menechmus de ijs multa. </s>
              <s xml:id="echoid-s21291" xml:space="preserve">dixere. </s>
              <s xml:id="echoid-s21292" xml:space="preserve">V eniam igitur ad id, quod quinto libro pollicitus ſum, & </s>
              <s xml:id="echoid-s21293" xml:space="preserve">modum ponam,
                <lb/>
                <note position="left" xlink:label="note-514.01.310-06" xlink:href="note-514.01.310-06a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
        </div>
      </text>
    </echo>