Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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[61.] III.
Page: 57 (37)
[62.] IV.
Page: 57 (37)
[63.] V.
Page: 57 (37)
[64.] VI.
Page: 57 (37)
[65.] VII.
Page: 57 (37)
[66.] VIII.
Page: 58 (38)
[67.] IX.
Page: 58 (38)
[68.] THEOR. XI. PROP. XIX.
Page: 58 (38)
[69.] COROLL. I.
Page: 64 (40)
[70.] COROLL. II.
Page: 64 (40)
[71.] COROLL. III.
Page: 64 (40)
[72.] COROLL. IV.
Page: 65 (41)
[73.] COROLL. V.
Page: 65 (41)
[74.] COROLL. VI.
Page: 65 (41)
[75.] PROBL. VI. PROP. XX.
Page: 66 (42)
[76.] COROLL. I.
Page: 67 (43)
[77.] COROLL. II.
Page: 68 (44)
[78.] PROBL. VII. PROP. XXI.
Page: 68 (44)
[79.] MONITVM.
Page: 69 (45)
[80.] THEOR. XII. PROP. XXII.
Page: 70 (46)
[81.] PROBL. VIII. PROP. XXIII.
Page: 71 (47)
[82.] PROBL. IX. PROP. XXIV.
Page: 73 (49)
[83.] PROBL. X. PROP. XXV.
Page: 74 (50)
[84.] PROBL. XI. PROP. XXVI.
Page: 75 (51)
[85.] SCHOLIVM I.
Page: 76 (52)
[86.] SCHOLIVM II.
Page: 76 (52)
[87.] PROBL. XII. PROP. XXVII.
Page: 77 (53)
[88.] PROBL. XIII. PROP. XXVIII.
Page: 78 (54)
[89.] PROBL. XIV. PROP. XXIX.
Page: 80 (56)
[90.] PROBL. XV. PROP. XXX.
Page: 81 (57)
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10278 tercepta applicatarum ſegmenta metitum, licet ſemper magis, ac magis de-
creſcat, eſſe tamen non minus interuallo 1 3, quod iuxta eaſdem æquidi-
ſtantes ordinatim ſectionibus applicatas, inter vtranque aſymptoton cadit.
Nam per ea, quæ infra demonſtrabimus, interuallum 2 1, maius eſt inter-
uallo 1 3. Pariter 4 5, eſt maius 6 7, communique addito 5 6, erit inter-
uallum 4 6, maius interuallo 5 7, ſiue 1 3, & hoc ſemper vbicunque ſu-
matur harum ſectionum interuallum infra applicatam 2 1 3. Quare hy-
perbolæ congruentes per diuerſos vertices ſimul adſcriptæ, licèt ſemper ma-
gis accedentes, ad interuallum nunquam perueniunt æquale cuidam dato
interuallo. Quod erat vltimò, & c.
COROLL.
EX his conſtat, congruentium Hyperbolarum non per eundem verticem
ſimul adſcriptarum aſymptotos eſſe inter ſe æquidiſtantes, & aſympto-
ton inſcriptæ ſecare Hyperbolen circumſcriptam.
Quod ſuperiùs promiſimus oſtendetur ſic.
SInt duæ congruentes Hyperbolæ KBC, DEF, per diuerſos vertices B, E
ſimul adſcriptæ, & circumſcriptæ KBC ſit centrum G, & aſymptotos
GI, inſcriptæ verò ſit centrum H, & aſymptotos HM, quæ ipſi GI æquidi-
ſtabit, per præcedens Coroll. ſitque applicata quæcunque IL vtranque
aſymptoton, & Hyperbolen ſecans in I, A, K, D, communemque diame-
trum in L: dico interceptum applicatę ſegmentum AD inſcriptæ Hyperbolę
DEF, maius eſſe intercepto eiuſdem applicatæ ſegmento IK inter aſympto-
ton, & circumſcriptam.
Ducta enim IM parallela ad GHO, & per
70[Figure 70] Mapplicata MNO, erunt IH, IO parallelo-
gramma, ac ideò tàm GH, quàm LO ipſi IM
æquales erunt, & inter ſe; quare addita com-
muni HL, erit GL æqualis HO, ſed eſt GB
æqualis HE, (cum ſint ſemi-tranſuerſa late-
ra congruentium Hyperbolarum) vnde reli-
qua BL, reliquæ EO æqualis erit, & ob id
ſemi-applicata LK ſemi-applicatę ON ęqua-
lis, ſed eſt tota LI æqualis totæ OM (cum ſint
oppoſitæ in parallelogrammo IO) ergo reli-
quæ KI, NM æquales erunt, ſed eſt 1110. h. maior NM, quare & eadem DA erit maior
KI. Quod erat, & c.

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