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

Table of contents

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[261.] Notæ in Propoſit. I.
Page: 312 (274)
[262.] Notæ in Propoſit. V. & XXIII.
Page: 313 (275)
[263.] SECTIO SECVNDA Continens Propoſit. II. III. IV. VI. & VII. Apollonij. PROPOSITIO II. & III.
Page: 314 (276)
[264.] PROPOSITIO IV.
Page: 315 (277)
[265.] PROPOSITIO VI. & VII.
Page: 316 (278)
[266.] Notæ in Propoſit. II. III.
Page: 317 (279)
[267.] Notæ in Propoſit. IV.
Page: 318 (280)
[268.] Notæ in Propoſit. VI. & VII.
Page: 319 (281)
[269.] SECTIO TERTIA Continens Propoſit. Apollonij VIII. IX. X. XI. XV. XIX. XVI. XVIII. XVII. & XX.
Page: 320 (282)
[270.] Notæ in Propoſit. VIII.
Page: 323 (285)
[271.] Notæ in Propoſit. IX.
Page: 324 (286)
[272.] Notæ in Propoſit. X.
Page: 325 (287)
[273.] Notæ in Propoſit. XI.
Page: 325 (287)
[274.] Notæ in Propoſit. XV.
Page: 326 (288)
[275.] Notæ in Propoſit. XIX.
Page: 326 (288)
[276.] Notæ in Propoſit. XVI.
Page: 327 (289)
[277.] Notæ in Propoſit. XVIII.
Page: 327 (289)
[278.] Notæ in Propoſit. XVII.
Page: 328 (290)
[279.] Notæ in Propoſit. XX.
Page: 328 (290)
[280.] SECTIO QVARTA Continens Propoſit. Apollonij XII. XIII. XXIX. XVII. XXII. XXX. XIV. & XXV.
Page: 329 (291)
[281.] Notæ in Propoſit. XII.
Page: 332 (293)
[282.] Notæ in Propoſit. XIII.
Page: 333 (294)
[283.] Notæ in Propoſit. XXIX.
Page: 334 (295)
[284.] Notæ in Propoſit. XXX.
Page: 334 (295)
[285.] Notæ in Propoſit. XIV. & XXV.
Page: 335 (296)
[286.] Notæ in Propoſit. XXVII.
Page: 335 (296)
[287.] SECTIO QVINTA Continens Propoſit. XXI. XXVIII. XXXXII. XXXXIII. XXIV. & XXXVII.
Page: 337 (298)
[288.] PROPOSITIO XXI. & XXVIII.
Page: 338 (299)
[289.] PROPOSITIO XXVI
Page: 339 (300)
[290.] PROPOSITIO XXXXII.
Page: 340 (301)
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page |< < (390) of 458 > >|
429390Archimedis ipſius A B, eſtque nota A D medietas differentiæ inter diametrum A C, & chor-
dam differentiæ F C; at propoſitio Archimedea verificatur in quolibet circuli
ſegmento ſiue maiori, ſiue minori; ex datis enim circumferentijs A C, A B,
493[Figure 493] A F, & F C vna cum cordis A C, & F C, haberi quidem poteſt chorda A B
paulo difficilius, ſi nimirum ex chorda A C tollatur chorda F C, & differen-
tia A E bifariam ſecetur in D, & ex arcu cognito B C datur angulus A, atque
angulus D rectus eſt, ergo triangulum A B D ſpecie notum erit, & propterea
proportio D A ad A B cognita erit, eſtque D A longitudine data, igitur A B
longitudine innoteſcet.
Notandum eſt quod figura appoſita in hac propoſ. non exprimit omnes caſus
propoſitionis, quandoquidem ſemicirculus eſt A B C, & propterea ex præceden-
tibus erroribus Arabici expoſitoris ſuſpicari licet non ritè eum percepiſſe Archi-
medis mentem.
PROPOSITIO IV.
A B C ſemicirculus, & fiant ſuper
494[Figure 494] A C diametrum duo ſemicirculi, quo-
rum vnus A D, alter vero D C, &
D B perpendicularis, vtique figura pro-
ueniens, quam vocat Archimedes AR-
BELON, eſt ſuperficies comprehenſa ab
arcu ſemicirculi maioris, & duabus cir-
cumferentijs ſemicirculorum minorum, eſt æqualis circulo, cuius
diameter eſt perpendicularis D B.
Demonſtratio. Quia linea D B media proportionalis eſt inter duas li-
neas D A, D C, erit planum A D in D C æquale quadrato D B, &
ponamus A D in D C cum duobus quadratis A D, D C communiter,
fiet planum A D in D C bis cum duobus quadratis A D, D C, nempe
quadratum A C, æquale duplo quadrati D B cum duobus quadratis A
D, D C, & proportio circulorum eadem eſt, ac proportio

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