Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
[141.] PROPOSITIO XXXIII. XXXIV.
Page: 163 (125)
[142.] PROPOSITIO XXXV.
Page: 163 (125)
[143.] PROPOSITIO XXXVI.
Page: 164 (126)
[144.] PROPOSITIO XXXVII. XLVI.
Page: 164 (126)
[145.] PROPOSITIO XXXVIII.
Page: 165 (127)
[146.] PR OPOSITIO XXXIX.
Page: 166 (128)
[147.] PROPOSITIO XXXX.
Page: 166 (128)
[148.] PROPOSITIO XXXXVII.
Page: 166 (128)
[149.] PROPOSITIO XXXXVIII.
Page: 167 (129)
[150.] Notæ in Propoſit. XXXII.
Page: 167 (129)
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page |< < (123) of 458 > >|
161123Conicor. Lib. V.
Notæ in Propoſ. XXIII. XXIV.
EContra linea maxima, ſi non egredia-
11a154[Figure 154] tur ex centro, continet cum mẽſura
angulum acutum, & proportio illius in-
uerſæ ad abſciſſam eius potentialis ex mẽ-
ſura cum origine, eſt vt proportio figuræ
recti. Si verò fuerit extra centrum, erit
perpendicularis ſuper rectum, & c. Mani-
feſtè nõ nulla in textu Arabicc deficiunt; ali-
qua verò immutari debent; alioquin propo-
ſitio vera non eſſet, itaque legendum puto: E
contra ſi maximi rami origo ponatur in axi
minore, & c: Vt in textu babetur.
Sit ſectio A B C elliptica, & E origo, & E F linea maxima, & c. Ad-
22b didi pariter in bac expoſitione verba, quæ deſiciunt; nimirum: Sit centrum
D, & origo E, quæ ſit in axi minori A C.
Et ideo D C ad dimidium erecti eſt linea minor, quàm D C, & ſit D
33c G ad G E, & c. Nonnulla adiungi debent buic textui corruptiſsimo, ne ſint
verba nil prorſus ſignificantia, itaque ſic legendum puto. Et ideo aliqua minor,
quàm D C ad reſiduam vſque ad E eandem proportionem babebit, quàm D C ad
ſemiſſem erecti; & ſit D G ad G E, & c. Quæ verba breuiſsimè more Apollonij
expoſita ſic confirmantur. Quia E C oſtenſa eſt minor dimidio erecti axis mi-
noris C A, fiat C K æqualis dimidio erecti; erit E C minor quàm C K,
& ablata communi D C erit D E minor, quàm K D; & propterea D E ad ean-
dem D C minorem proportionem babebit, quàm K D: fiat E D a d D G, vt K
D ad D C, erit D G minor, quàm D C: & componendo, E G ad G D eandem
proportionem babebit, quàm K C ad C D, & inuertendo, D G ad G E eandem
proportionem babebit, quàm D C ſemiſsis axis recti ad C K ſemiſsim erecti
eiuſdem axis; & ex G ducatur G F perpendicularis ad axim, quàm, dico, oc-
currere ſectioni in F termino maximi rami E F.
Et ſi maxima fuerit extra centrum, vt D B erit perpendicularis, & c.
44d Textus euidenter corruptus ſic corrigi debet. Si verò ramus maximus educatur
ex centro, vt D B, & c.
Notæ in Propoſ. XXXV.
SI producatur vna linearum maximarum, vt E B ad latus illius originis
55a E ad punctum F, fiet maxima linearum egredientium ab illo puncto
F G, F H, F I, F A ad ſectionem B I A in directum, & propinquior illi
maior eſt remotiore, & c. Immutaui nonnulla, quæ ad propoſitionis integrita-
tem facerc videbantur: vt in textu babetur.

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