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

Iam ſi iungantur AN, AO, AP, & c. quæ ſecent LO, MP, FG, & c. in 5, 6,
7, & c. incerceptæ N5, O6, P7, cadent totæ intra Parabolen AGC, hoc eſt
extra trilineum AGCB; & ſi ex punctis B, Q, R, K, & c. ducantur contin-
gentes BS, QT, RV, KX, & c. ipſæ æquidiſtabunt rectis CD, N5, O6, P7,
& c. (cum ductæ AC, AN, AO, AP, & c. ſint ordinatim ductæ 113. Co-
roll. 13. h. BC, QN, RO, KP, & c) ſicque circumſcribetur trilineo AHBCGA, figura
ex æquealtis parallelogrammis BD, S5, T6, V7, & c.

Ampliùs, ſi ipſæ ZQ, & R, IK, & c. producantur extra ſemi-Parabolen,
cadent totæ intra trilineum AEBH, atque ita inſcribetur ei figura ex paralle-

30[Figure 30] logrammis & c. Et ſi ex punctis Q, R, K, & c. ducantur contingentibus SB
TQ, VR, & c. æquidiſtantes, cadent totæ intra trilineum AHBCG, cum ſint
ordinatim ductæ, & ſi ex punctis N, O, P, & c. ducantur ad partes diametri
EBC rectæ æquidiſtantes ipſis AC, AN, AO, & c. (quæ erunt etiam paral-
lelæ contingentibus ex B, Q, R, & c. vel prædictis applicatis ex Q, R, K & c.)
cadent hæ@ quoq; intra trilineum AHBCG, nam quæ ex N ducitur ipſi AC
æquidiſtans ad partes diametri CB cadit extra Parabolen AGNC, cum ſit
AD maior DC, & quæ ex O ęquidiſtat ipſi AN cadit extra AGC, cum ſit AS
maior 5N, & ſic de reliquis. Itaq; hac operatione inſcribetur trilineo AH-
BCG figura ex parallelogrãmis æquealtis, & c. Quare ex his, & ex 14.

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