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

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 figures

[Figure 161]

[Figure 162]

[Figure 163]

[Figure 164]

[Figure 165]

[Figure 166]

[Figure 167]

[Figure 168]

[Figure 169]

[Figure 170]

[Figure 171]

[Figure 172]

[Figure 173]

[Figure 174]

[Figure 175]

[Figure 176]

[Figure 177]

[Figure 178]

[Figure 179]

[Figure 180]

[Figure 181]

[Figure 182]

[Figure 183]

[Figure 184]

[Figure 185]

[Figure 186]

[Figure 187]

[Figure 188]

[Figure 189]

[Figure 190]

154116Apollonij Pergæi

143[Figure 143]

Ergo quadratum I C æquale eſt duplo trianguli N F M cum duplo
11e trianguli D I N, & c. Quoniam quadratum I C æquale eſt duplo trianguli I
C F, ſeu duplo trianguli I F E vna cum duplo trianguli E F C; eſtque duplum
trianguli E D M æquale duplo trianguli E C F; igitur quadratum I C æquale
eſt duplo trianguli I F E vna cum duplo trianguli E M D: ĳs vero triangulis
æquatur duplum trianguli N F M vna cum duplo trianguli D I N; igitur qua-
dratum I C æquale eſt duplo trianguli N F M vna cum duplo trianguli D I N:
eſt vero quadratum I D æquale duplo trianguli D I N; igitur exceſſus quadrati
I C ſupra quadratum I D eſt triangulum N F M bis ſumptum; ſcilicet exem-
plar applicatum ad latus tranſuerſum D C.

SECTIO DECIMASEPTIMA
Continens XIX. XX. XXI. XXII. XXIII.
XXIV. & XXV. Propoſ. Apollonij.

PROPOSITIO XIX.

SI menſura E C ſumatur in axe minori ellipſis A B C, ſitque
22a maior comparata; erit maximus omniũ ramorũ egredientiũ
ex ſua origine, vt E F, E B, E G; & maximo propinquior,
maior erit remotiore, nempe E F, quàm E B, & E B, quàm E G.

Coniungamus rectas A G, G B, B F,

144[Figure 144]33b F C; & ſecetur C H æqualis compara-
tæ: iungãturque F H, H B, H G.

Et quoniam H C maior eſt, quàm H
F, (16. 17. 18. ex 5.) erit angulus H C
F minor, quàm H F C; & ideo multo
minor erit, quàm E F C, quare E C
maior eſt, quàm E F: & ſic conſtat, quod
E F maior ſit, quàm E B, & E B, quàm
E G, & E G, quàm A E; quod erat
oſtendendum.

Text layer

Text normalization

Search