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 Notes

< >
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
[Note]
< >
page |< < (186) of 458 > >|
224186Apollonij Pergæi
LEMMA VIII.
SI duo hyperbolica, aut elliptica ſegmenta A B C, D E F fuerint
ſimilia, quorum baſes A C, D F efficiant cum diametrorum ab-
ſciſsis B M, E O angulos æquales M, &
O; ſintque eorum tranſ-
uerſa latera T B, Z E, recta vero B L, E Q.
Dico figuras eorum;
ſiue rectangula T B L, & Z E Q ſimilia eße.
Secentur ſegmentorum abſciſſæ M B, O E proportionaliter in N, P, & per
ea puncta ducantur ordinatim ad diametros applicatæ G N, I P æquidiſtantes
baſibus, efficientes abſciſſas B N, E P, coniunganturq;
duæ rectæ lineæ T L, Z
Q ſecantes rectas lineas N H, M V, P K, O S æquidiſtantes lateribus rectis B
L, E Q in punctis H, V,
251[Figure 251] K, S, atque à punctis H, &

K ducantur rectæ lineæ H X,
K R parallelæ diametris occur-
rentes ipſis M V, O S in X,
11Defin. 7.
huius.
&
R. Quoniam ſegmenta ſup-
ponuntur ſimilia erit A M ad
M B, vt D O ad O E, &
G
N ad N B erit vt I P ad P
E, atque quadratum A M, ſeu
ei æquale rectangulum B M V,
2212. 13.
lib. 1.
ad quadratum M B eandem
proportionem habebit, quàm,
33Ibidem. quadratum D O, ſeu ei æquale
rectangulum E O S ad quadratum O E;
ſed vt rectangulum B M V ad quadra-
tum M B ita eſt M V ad M B (cum M B ſit eorum altitudo communis) pari-
terque vt rectangulum E O S ad quadratum O E, ita eſt O S ad O E;
quare
M V ad M B eandem proportionem habebit, quàm O S ad O E;
non aliter oſten-
detur N H ad N B eandem proportionem
252[Figure 252] habere, quàm P K ad P E:
erat autem
44Lem. 1.
lib. 5.
M B ad B N vt O E ad E P;
ergo compa-
rando antecedentes, &
poſtea conſequentes
ad differentias terminorum erit B M ad M
N vt E O ad O P;
atque B N ad N M eã-
dem proportionem habebit, quàm E P ad P
O.
Quare ex æquali V M ad M N erit vt
S O ad O P, atque H N ad N M erit vt K
P ad P O;
& differentia ipſarum V M &
H N ideſt X V ad M N, ſeu ad X H ean-
dem proportionem habebit, quàm differentia ipſarum S O, &
K P, ideſt S R
ad O P, ſeu ad R K;
quapropter V X ad X H erit vt S R ad R K; ſed quia
X V, L B inter ſe, nec non X H, &
B T ſunt parallelæ, atq; etiam S R, Q E
inter ſe, nec nõ R K, &
E Z ſunt æquidiſtantes; erunt triangula V X H, & L

Text layer

  • Dictionary

Text normalization

  • Original

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index