Vitruvius, De architectura libri decem, 1567

Table of figures

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[131] a b g. concentricum. d. eius centrũ.t z. eccentricum.h. eius centrum.e z. epicyclus.g. eius centrum.d b. & g z. œquales.d z. parallelogrammum.motus {concentrici a d g. \\ epicycli e g z. \\ eccentrici t b z. uet t dg. \\ iugieccentric. a d t. anguli t b z. & e g z. œqua-les ſunt.angulus a d g. œqualis augulis. {adt. \\ adg. f n b a d o k
[132] b k epicyclus.b. centrum eius.h. uigum.n. Antijugum epicycli.k. punctũ primœ morœ.c. mundi centrum.o. punctũ ſecundæ morœ.h l k. arcus primœ mo rœ.k n o. arcus regreſſus-o b k. arcus directio-nis. L K A H B N O C
[133] Porfioni del cerchio che fannoſe s̃teſſe torno dlaTramòntanaTram ontanaSlmiſifudineTramonſangCarro che uoſge infomoalla Framonlana
[134] a b c d f
[135] A. ſectio parabole.B. vestigium. C. parabole.G. ſectio ellipſis.D. ſectio hyperbole.E. vestigium F. hyperbole. a f a f 1 f f f 1 2 1 1 2 3 2 2 3 4 3 3 4 5 4 4 5 6 C 5 5 6 F 7 A 6 6 8 7 8 7 7 D 8 9 8 8 9 10 11 10 10 11 11 11 11 b 12 g e d b e h d gf g b 6 7 3 1 2 4 6 8 10c g b E a 11 9 7 3 3 1 d 2 4 6 8 10 e ha f 1 2 3 4 5 6 7 8 9 10 11 a b c d 9 8 7 6 3 2 1 f b a H d g 10 9 8 7 6 5 4 3 2 1 ff 1 2 3 4 5 6 7 8 9 10 11 g
[136] m q 0 s k h c b s n L I p q s
[137] Il polo.cqiunot.orizonte c e b a f
[138] l n k mcridl. parte delverno E e h a s i 9 8 7 6 5della jtate 4 3 parte g h f x lacato manaco b r c linca del.piano t
[139] Analemmatis figura.MERIDIAN: S. M. MLSLACITREVM.M.MERIDIAN: .S.OMVERTICAV.M..S.. O. M.ORIZON:W. A.STAB:
[140] 11 ſ x d 11 p k 1 2 1 2 3 4 5f 6 r 11 10 9 8 7 n f m 12 11 10 9 8 7 6 5 1 02 3 4 1g c 1 2 1 2 3 4 5 6 e 11 10 9 8 7 q b o
[141] 1 3 b x z g 2 5 f p 0 1 4 t I c e o n m r u 6 q i h 8 y d 5
[142] 5 4 b 3 2 7 8 9 10 f 6 5 7 1 11 6 5 7 9 4 4 8 8 N 9 x 12 1 11 2 10 3 9 4 8 5 7 3 39 9 F 6 g 2 2 10 10 o a @ d 1 11 7 6 z 1 11 8 6 7 c 1 12 10 1@ 1 2 1 1 11 11 5 11 2 2 10 21 11 b f @ 8 3 3 9 9 12 1 4 5 g 6 10 8 11 1 9 10 2 2 2 10 5 7 2 z 9 c 8 4 7 5 9 3 10 4 8 8 4 3 7 2 10 7 5 9 3 1 11 12 8 4 11 1 10 2 0 @ d 7 5 9 3 I 8 4 7 5 6 c &
[143] 5 6 7 4 8 3 9 2 10 1 11 4 8 3 9 d d 2 3 4 5 6 7 8 9 10 10 1 1 v n c
[144] 12 1 1 1111 2 2 10 10 3 3 9 9 4 4 8 8 5 5 7 7 6 6 6 T 7 7 5 5 8 8 4 4 9 9 3 3 10 10 2 2 11 11 1 1 12
[145] 11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 11 1 2 3 10 4 5 E 6 6 7
[146] 9 3 4 2 8 10 11 12 1 5 7 6 6 G
[147] 8 9 10 7 6 5 11 1 8 1 11 F
[148] 16 15 17 14 14 18 19 19 13 13 20 20 12 12 21 21 11 11 H 22 22 10 10 23 23 9 9 24 16 16 23 23 17 17 22 22 18 18 21 21 29 20
[149] 19 20 21 18 17 22 23 17 16 18 17 9 15 14 13 11 13 20 16 12 21 17 20 22 21 11 22 10 23 9 18 L 17 18 19
[150] 23 17 22 16 18 9 21 23 19 10 19 20 22 11 21 20 13 19 14 18 15 17 16 K
[151] 17 18 19 20 21 22 16 23 15 14 13 12 11 10 11 12 21 22 10 9 23 M
[152] Q K r n r 12 11 K 2 2 @ 4 p 8 7 e t 8 9 c P 7 4 3 10 7 @ P 5 q P 6 2 8 7 q P t t 11 1 I 1 11 7 q p 2 10 q p 3 9 @ a e b 4 8 2 7 6 5 P 10 6 f P 9 3 8 4 f P 1 f P 11 10 2 a f b e 4 9 3 11 10 2 11 1 11 1 u m 12 15 @ d 12 4 5 m 3 4 5 7 8 9 d @ 2 @ 0 10 2 11 1 a 0 s 7 1 n P p 5 6 7 10 6 6 6 3 4 8 9 7 e 5 5 7 4 5 3 10 11 12 1 2 3 8 9 3 1 e H 23 10 22 24 23 22 15 16 17 18 19 21 13 14 20
[153] Horologia in plano meridiani.6 5 4 3 2 1 7 8 9 10 11 12 u l d 7 4 8 3 9 2 10 b n n n n n 5 4 3 2 1 a c e c y n n n n n p 1 2 3 4 5 n ſ ſ 4 3 2 1 r 4 3 2 1 e 4 3 2 1 B 9 10 11 12 13 14 e H 5 6 7 8 9 10 11 e E g r 7 6 5 4 3 2 1 F g d 23 22 21 20 19 18 18 c g G d f a b e g c 1 2 3 4 5 4 3 2 1 8 7 6 5 4 3 2 1 f D e 11 10 19 18
[154] Horologia in plano æquinoctialis.d b 5 6 7 4 8 9 3 g f k L @ m 2 10 l 8 1 11 a e b B L 1 f k m h @ z r s 1 n 11 A 2 1 10 12 3 9 11 1 4 8 10 1 2 5 6 7 b d 9 3 8 4 7 5 6 c 6 7 5 8 4 9 3 18 17 16 10 2 16 17 18 19 11 12 1 19 20 14 14 20 21 13 13 21 22 12 12 22 23 11 23 24 24 14 14 23 15 23 22 15 22 16 16 21 17 21 20 19 18 17 18 19 20
[155] 12 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1
[156] Instrumenta è regione poſita ſeruiunt fronti horologij ſequentis, illud uero inſerius eſt immobil-le ad aliud, & aliud ab artiſicio aquæ mouetur.B 270 A 360 stella.p.@ f 180 C 10 hircuſ@ 20 30 40 x cani ſminor* 50 60 70 80 90 C@nis Maior* D
[157] 6 5 7 4 8 3 9 2 10 1 11 12 T R 12 L 11 1 A f C 10 2 9 3 8 4 7 5 6
[Figure 158]
[Figure 159]
[Figure 160]
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            <p>
              <s xml:id="echoid-s26736" xml:space="preserve">
                <pb o="356" file="514.01.388" n="388" rhead="LIBER"/>
              erit in eius capitulo digitorum. </s>
              <s xml:id="echoid-s26737" xml:space="preserve">5. </s>
              <s xml:id="echoid-s26738" xml:space="preserve">ſi pondo quatuor, digitorum 6. </s>
              <s xml:id="echoid-s26739" xml:space="preserve">ſi octo, digitorum 7. </s>
              <s xml:id="echoid-s26740" xml:space="preserve">*** de-
                <lb/>
              cempondo digitorum 8. </s>
              <s xml:id="echoid-s26741" xml:space="preserve">*** uiginti pondo digitorum. </s>
              <s xml:id="echoid-s26742" xml:space="preserve">10. </s>
              <s xml:id="echoid-s26743" xml:space="preserve">*** quadraginta pondo digitorum
                <lb/>
                <emph style="sc">XII.</emph>
              S. </s>
              <s xml:id="echoid-s26744" xml:space="preserve">K. </s>
              <s xml:id="echoid-s26745" xml:space="preserve">ſexaginta pondo, digitorum
                <emph style="sc">XIII.</emph>
              & </s>
              <s xml:id="echoid-s26746" xml:space="preserve">digiti octaua parte, octuaginta pondo, digito-
                <lb/>
              rum
                <emph style="sc">XV.</emph>
              *** centum uigintipondo pedis I. </s>
              <s xml:id="echoid-s26747" xml:space="preserve">S. </s>
              <s xml:id="echoid-s26748" xml:space="preserve">& </s>
              <s xml:id="echoid-s26749" xml:space="preserve">ſeſquidigiti *** centum, & </s>
              <s xml:id="echoid-s26750" xml:space="preserve">ſexaginta pondo,
                <lb/>
              pedum
                <emph style="sc">II.</emph>
              *** centum & </s>
              <s xml:id="echoid-s26751" xml:space="preserve">octuaginta pondo pedum
                <emph style="sc">II.</emph>
              & </s>
              <s xml:id="echoid-s26752" xml:space="preserve">digitorum
                <emph style="sc">V.</emph>
              ducenta pondo pedum
                <lb/>
                <emph style="sc">II.</emph>
              & </s>
              <s xml:id="echoid-s26753" xml:space="preserve">digitorum
                <emph style="sc">VI.</emph>
              ducenta decem pondo pedum
                <emph style="sc">II.</emph>
              & </s>
              <s xml:id="echoid-s26754" xml:space="preserve">digitorum
                <emph style="sc">VII.</emph>
              ***
                <emph style="sc">Cci</emph>
              . </s>
              <s xml:id="echoid-s26755" xml:space="preserve">pon-
                <lb/>
              do
                <emph style="sc">XI.</emph>
              S.</s>
              <s xml:id="echoid-s26756" xml:space="preserve"/>
            </p>
            <p style="it">
              <s xml:id="echoid-s26757" xml:space="preserve">Quoniam balistis ingentia ſaxorum pondera torqueb antur, ideo maiori apparatu, quam in catapultis opus
                <lb/>
                <handwritten xlink:label="hd-514.01.388-1" xlink:href="hd-514.01.388-1a" number="70"/>
              erat. </s>
              <s xml:id="echoid-s26758" xml:space="preserve">Cæterum & </s>
              <s xml:id="echoid-s26759" xml:space="preserve">in ipſis haliſtis diſcrimina ſunt, licent ad unum effctum omnes comparentur. </s>
              <s xml:id="echoid-s26760" xml:space="preserve">Diſcrimina illa
                <lb/>
              ex ponderum mittendorum diuerſitate ſumuntur, hinc eſt quod aliæ uectibus, & </s>
              <s xml:id="echoid-s26761" xml:space="preserve">ſuculis, quæ ſcilicet minora
                <lb/>
                <note position="left" xlink:label="note-514.01.388-01" xlink:href="note-514.01.388-01a" xml:space="preserve">10</note>
              ſaxa mittunt, nonnullæ trochleis multorum orbiculorum, aliæ ergatis, quædam etiam tympanis tor queantur.
                <lb/>
              </s>
              <s xml:id="echoid-s26762" xml:space="preserve">Balista igitur omnis ad propoſitam magnitudinem ponderis ſaxi, quod id organum mittere debet, perficienda
                <lb/>
              est. </s>
              <s xml:id="echoid-s26763" xml:space="preserve">Verum ea tatio non eſt omnibus expedita, niſi enim Geometria, & </s>
              <s xml:id="echoid-s26764" xml:space="preserve">Arithmetica adfuerit, uanus erit
                <lb/>
              labor, quoniam periculum eſt ne in eum errorem incidamus, quem illi incidere, qui cum cubum duplicare in-
                <lb/>
              stituiſſent, octuplum ſecere. </s>
              <s xml:id="echoid-s26765" xml:space="preserve">ita enim ſi ex hoc principio, quod experientia, & </s>
              <s xml:id="echoid-s26766" xml:space="preserve">obſeruatione inualuit, ut ſi dua-
                <lb/>
              pondo ſaxum quinum digitum ſoramen quærat, quis ratiocinetur quatuorpondo ſaxum denum digitum fora-
                <lb/>
              men habere debere, falletur demum ut pluſquam centum pedum ſunis, ſeu foraminis diametrum ſiciat, ſi ſa-
                <lb/>
              xum ducentorum & </s>
              <s xml:id="echoid-s26767" xml:space="preserve">quinquaginta pondo uelit torquere. </s>
              <s xml:id="echoid-s26768" xml:space="preserve">Cum neceſſe ſit ( ut ait Eratoſthenes ad Ptolomæum
                <lb/>
              regem in epiſtola, ſuperiori libro citata ) omnia proportione augeri, craſſitudines, magnitudines, foramina,
                <lb/>
              modtolos, & </s>
              <s xml:id="echoid-s26769" xml:space="preserve">neruos ingredientes, quæ ſine mediarum comparabilium inuentione fieri non poſſunt. </s>
              <s xml:id="echoid-s26770" xml:space="preserve">Atque
                <lb/>
                <note position="left" xlink:label="note-514.01.388-02" xlink:href="note-514.01.388-02a" xml:space="preserve">20</note>
              hæc nos iuuabunt, ſi Geometricis rationibus uti uelimus. </s>
              <s xml:id="echoid-s26771" xml:space="preserve">Sumatur enim diameter funis, ſeu ſoramiuis baliſtæ
                <lb/>
              quæ duapondo ſaxum mittere debet, & </s>
              <s xml:id="echoid-s26772" xml:space="preserve">ſit linea a b. </s>
              <s xml:id="echoid-s26773" xml:space="preserve">& </s>
              <s xml:id="echoid-s26774" xml:space="preserve">ſumatur linea c d. </s>
              <s xml:id="echoid-s26775" xml:space="preserve">dupla ipſi a b. </s>
              <s xml:id="echoid-s26776" xml:space="preserve">& </s>
              <s xml:id="echoid-s26777" xml:space="preserve">iuxta
                <lb/>
              aliquem modum ex ſupradictis in nono libro mediarum inueniendarum, capiantur mediæ comparabiles, & </s>
              <s xml:id="echoid-s26778" xml:space="preserve">ha
                <lb/>
              bebitur diameter funis baliſtæ, quæ quatuor pondo ſaxum mittere debet. </s>
              <s xml:id="echoid-s26779" xml:space="preserve">Verum ſinumeris ea ratio quærenda
                <lb/>
              eſt, ut Græci monent, ita erit ſciendum ut etiam animaduertit Ioannes Buteo qui ſic ait. </s>
              <s xml:id="echoid-s26780" xml:space="preserve">Cum lapis duapon-
                <lb/>
              do foramen habe at digitorum quinque, quæritur ad lapidem quatuor pondo quot digitorum debeat eſſe ſora-
                <lb/>
              men? </s>
              <s xml:id="echoid-s26781" xml:space="preserve">ad cubum redige 5. </s>
              <s xml:id="echoid-s26782" xml:space="preserve">hoc est ducas in ſe, postea in productum, fit cubus 125. </s>
              <s xml:id="echoid-s26783" xml:space="preserve">cum itaque uideas ad
                <lb/>
              duapondo diametrum ſoraminis dari, quæ ſua cubicatione producat 125. </s>
              <s xml:id="echoid-s26784" xml:space="preserve">ratione ſequitur, ut ad quatuor
                <lb/>
              pondo, quod eſt duplum 2. </s>
              <s xml:id="echoid-s26785" xml:space="preserve">tanta diametros adhibeatur, quæ ſua etiam cubicatione compleat numerum 250.
                <lb/>
              </s>
              <s xml:id="echoid-s26786" xml:space="preserve">qui duplus eſt cubi 125. </s>
              <s xml:id="echoid-s26787" xml:space="preserve">Sed quia 250 non eſt cubus ipſius, quod quæritur ad diametron, latus perfecte
                <lb/>
                <note position="left" xlink:label="note-514.01.388-03" xlink:href="note-514.01.388-03a" xml:space="preserve">30</note>
              dari non potest in numeris, cum non ſit in rerum natura. </s>
              <s xml:id="echoid-s26788" xml:space="preserve">Supereſt igitur ut huic propinquum numerum ra-
                <lb/>
              tiocinando diſquiras, quem inuenies eſſe maiorem quam 6. </s>
              <s xml:id="echoid-s26789" xml:space="preserve">quod eſt latus cubi 216. </s>
              <s xml:id="echoid-s26790" xml:space="preserve">maiorem etiam quam
                <lb/>
              ſex & </s>
              <s xml:id="echoid-s26791" xml:space="preserve">parte quarta, minorem autem, quàm ſex, & </s>
              <s xml:id="echoid-s26792" xml:space="preserve">tertia. </s>
              <s xml:id="echoid-s26793" xml:space="preserve">Ex his particulis tertia ſcilicet, & </s>
              <s xml:id="echoid-s26794" xml:space="preserve">quarta ſum-
                <lb/>
              pto dimidio, quod eſt ſeptem quartædecimæ, iunctoq; </s>
              <s xml:id="echoid-s26795" xml:space="preserve">ad ſex numerum habetis ſenarium, cum ſeptem uigeſimis
                <lb/>
              quartis, adeo ueritati propinquum, ut inde nullus, de quo ſit curandum, error oriri poſſit. </s>
              <s xml:id="echoid-s26796" xml:space="preserve">nam cubus lateris
                <lb/>
              ſex & </s>
              <s xml:id="echoid-s26797" xml:space="preserve">ſeptem uigeſimæ quartæ, est 249. </s>
              <s xml:id="echoid-s26798" xml:space="preserve">& </s>
              <s xml:id="echoid-s26799" xml:space="preserve">ex particulis 13824. </s>
              <s xml:id="echoid-s26800" xml:space="preserve">775. </s>
              <s xml:id="echoid-s26801" xml:space="preserve">dicimus itaque in balista, quæ
                <lb/>
              quatuor pondo mittere debet, ſoramen in eius capitulo fieri debere digitorum ſex, &</s>
              <s xml:id="echoid-s26802" xml:space="preserve">digiti ſeptem uigeſimiſ-
                <lb/>
              quartis. </s>
              <s xml:id="echoid-s26803" xml:space="preserve">Inquiramus autem lapidis decempondo foramen: </s>
              <s xml:id="echoid-s26804" xml:space="preserve">cum igitur hoc pondus ad duapondo ſit quincuplũ
                <lb/>
              ita & </s>
              <s xml:id="echoid-s26805" xml:space="preserve">cubum ſoraminis ipſius, ad cubum foraminis alterius, quincuplum eſſe oportet. </s>
              <s xml:id="echoid-s26806" xml:space="preserve">neque enim aliter in-
                <lb/>
              stituta proportio conſtat. </s>
              <s xml:id="echoid-s26807" xml:space="preserve">propterea iam poſitum cubum 125. </s>
              <s xml:id="echoid-s26808" xml:space="preserve">multiplico per 5. </s>
              <s xml:id="echoid-s26809" xml:space="preserve">& </s>
              <s xml:id="echoid-s26810" xml:space="preserve">colligo 625. </s>
              <s xml:id="echoid-s26811" xml:space="preserve">poſſum
                <lb/>
                <note position="left" xlink:label="note-514.01.388-04" xlink:href="note-514.01.388-04a" xml:space="preserve">40</note>
              etiam ad hoc ratiocinando regulam adhibere dicendo ſi pondo 2. </s>
              <s xml:id="echoid-s26812" xml:space="preserve">fiat 10. </s>
              <s xml:id="echoid-s26813" xml:space="preserve">quid 125. </s>
              <s xml:id="echoid-s26814" xml:space="preserve">Age multiplicando
                <lb/>
              125. </s>
              <s xml:id="echoid-s26815" xml:space="preserve">in 10. </s>
              <s xml:id="echoid-s26816" xml:space="preserve">& </s>
              <s xml:id="echoid-s26817" xml:space="preserve">productum. </s>
              <s xml:id="echoid-s26818" xml:space="preserve">1250. </s>
              <s xml:id="echoid-s26819" xml:space="preserve">partireper 2. </s>
              <s xml:id="echoid-s26820" xml:space="preserve">idemq; </s>
              <s xml:id="echoid-s26821" xml:space="preserve">quod prius inuenies, ſcilicet. </s>
              <s xml:id="echoid-s26822" xml:space="preserve">625. </s>
              <s xml:id="echoid-s26823" xml:space="preserve">Huius
                <lb/>
              cubitum latus, ad uerem accedens proxime eſt 8. </s>
              <s xml:id="echoid-s26824" xml:space="preserve">& </s>
              <s xml:id="echoid-s26825" xml:space="preserve">undecim uigeſimæ, unde prouenit cubus 625. </s>
              <s xml:id="echoid-s26826" xml:space="preserve">& </s>
              <s xml:id="echoid-s26827" xml:space="preserve">
                <lb/>
              211. </s>
              <s xml:id="echoid-s26828" xml:space="preserve">octomilenas. </s>
              <s xml:id="echoid-s26829" xml:space="preserve">Inuentum igitur ad lapidem pondo decem aptandum eſſe foramen digitorum octo, cum
                <lb/>
              undecim uigeſimis. </s>
              <s xml:id="echoid-s26830" xml:space="preserve">Quæ quidem particula digiti ſemiſſem excedit una uigeſima. </s>
              <s xml:id="echoid-s26831" xml:space="preserve">& </s>
              <s xml:id="echoid-s26832" xml:space="preserve">ſic ad omne datum pon-
                <lb/>
              dus rationibus cubicis ſoramina inueſtigari poſſunt. </s>
              <s xml:id="echoid-s26833" xml:space="preserve">Sed in his, quæ ab authore ponutur, demptis primo, & </s>
              <s xml:id="echoid-s26834" xml:space="preserve">
                <lb/>
              ultimo non niſi ſecundum proximitatem inuentio procedit quod & </s>
              <s xml:id="echoid-s26835" xml:space="preserve">intelligentiæ difficultatem, & </s>
              <s xml:id="echoid-s26836" xml:space="preserve">ratiocina-
                <lb/>
              tioni moleſtiam affert. </s>
              <s xml:id="echoid-s26837" xml:space="preserve">In multis tamen numeri for aminum perſecte conuniunt, ut pote ſi detur lapis pondo
                <lb/>
              ſexdecim for amen erit digitorum decem. </s>
              <s xml:id="echoid-s26838" xml:space="preserve">Quoniam cubus lateris 10. </s>
              <s xml:id="echoid-s26839" xml:space="preserve">quieſt 1000. </s>
              <s xml:id="echoid-s26840" xml:space="preserve">ad cubum lateris 5.
                <lb/>
              </s>
              <s xml:id="echoid-s26841" xml:space="preserve">qui est 125. </s>
              <s xml:id="echoid-s26842" xml:space="preserve">rationem habet, quam pondo ſesxdecim, ad duapondo, ideſt octuplam. </s>
              <s xml:id="echoid-s26843" xml:space="preserve">Item ad pondo 54. </s>
              <s xml:id="echoid-s26844" xml:space="preserve">ſo-
                <lb/>
                <note position="left" xlink:label="note-514.01.388-05" xlink:href="note-514.01.388-05a" xml:space="preserve">50</note>
              ramen erit digitorum quindecim ad pondo, 128. </s>
              <s xml:id="echoid-s26845" xml:space="preserve">digitorum 20. </s>
              <s xml:id="echoid-s26846" xml:space="preserve">hoc eſt pedis nuius, cum quadrante. </s>
              <s xml:id="echoid-s26847" xml:space="preserve">Ad
                <lb/>
              pondo 250. </s>
              <s xml:id="echoid-s26848" xml:space="preserve">quod eſt maximum in Vitruuio, pedis unius cum nouem digitis. </s>
              <s xml:id="echoid-s26849" xml:space="preserve">Docet præterea idem author,
                <lb/>
              quod datis quibuſlibet for aminum numeris, omne etiam pondus ipſorum in numeris dabitur abſolutè. </s>
              <s xml:id="echoid-s26850" xml:space="preserve">quorum
                <lb/>
              aliquot exempla ſubijcit. </s>
              <s xml:id="echoid-s26851" xml:space="preserve">Eſto foramen in balista digitorum ſex, cujus lapidem oporteat inuentire. </s>
              <s xml:id="echoid-s26852" xml:space="preserve">Accipe duos
                <lb/>
              cubos laterum 5. </s>
              <s xml:id="echoid-s26853" xml:space="preserve">& </s>
              <s xml:id="echoid-s26854" xml:space="preserve">6. </s>
              <s xml:id="echoid-s26855" xml:space="preserve">qui ſunt. </s>
              <s xml:id="echoid-s26856" xml:space="preserve">125. </s>
              <s xml:id="echoid-s26857" xml:space="preserve">& </s>
              <s xml:id="echoid-s26858" xml:space="preserve">216. </s>
              <s xml:id="echoid-s26859" xml:space="preserve">& </s>
              <s xml:id="echoid-s26860" xml:space="preserve">ita rationcinare. </s>
              <s xml:id="echoid-s26861" xml:space="preserve">Si 125. </s>
              <s xml:id="echoid-s26862" xml:space="preserve">fit 216. </s>
              <s xml:id="echoid-s26863" xml:space="preserve">quid duapon-
                <lb/>
              do? </s>
              <s xml:id="echoid-s26864" xml:space="preserve">& </s>
              <s xml:id="echoid-s26865" xml:space="preserve">productum partiens in 125. </s>
              <s xml:id="echoid-s26866" xml:space="preserve">prouenietq́; </s>
              <s xml:id="echoid-s26867" xml:space="preserve">357. </s>
              <s xml:id="echoid-s26868" xml:space="preserve">dicemus igitur foramini digitorum ſex deberi da-
                <lb/>
              pidem trapondo cum particula 125. </s>
              <s xml:id="echoid-s26869" xml:space="preserve">quæ quidem paulo maior eſt quincunce. </s>
              <s xml:id="echoid-s26870" xml:space="preserve">& </s>
              <s xml:id="echoid-s26871" xml:space="preserve">hoc modo datis foramini-
                <lb/>
              bus lapidum grauitatem ſemper habebis: </s>
              <s xml:id="echoid-s26872" xml:space="preserve">ut in ſemipedali foramine lapis erit octopondo cum 24. </s>
              <s xml:id="echoid-s26873" xml:space="preserve">centeſi-
                <lb/>
              mis uigeſimis quintis. </s>
              <s xml:id="echoid-s26874" xml:space="preserve">Inſemipedali, & </s>
              <s xml:id="echoid-s26875" xml:space="preserve">unius digiti pondo 11. </s>
              <s xml:id="echoid-s26876" xml:space="preserve">cum 83. </s>
              <s xml:id="echoid-s26877" xml:space="preserve">centum uigeſimis quintis in peda-
                <lb/>
              li pondo 65. </s>
              <s xml:id="echoid-s26878" xml:space="preserve">cum 67. </s>
              <s xml:id="echoid-s26879" xml:space="preserve">centum uigeſimis quintis, in palmo pedali centum uiginit octo, in ſeſquipedali pon-
                <lb/>
                <note position="left" xlink:label="note-514.01.388-06" xlink:href="note-514.01.388-06a" xml:space="preserve">60</note>
              </s>
            </p>
          </div>
        </div>
      </text>
    </echo>