Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

G, H cum ſit vna applicatarum, & c.) interiorem ſecans in D, F. Dico re-
ctangulum ſub ſegmentis G D, D H æquari quadrato ſemi-tangentis A E.

283.1.

Coroll.
45. h.

Nam iuncta D E, & bifariam ſecta in N, ducatur eius diameter N O P,
quæ erit vtriuſque ſectionis diameter (cum ipſę ponantur parallelę, vel con-
centricæ) eas ſecans in O, P. Patet, ſi ex O, P concipiantur contingentes
ſectiones O V, P Q has inter ſe æquidiſtare, ſed O V ipſi D E ęquidiſtat, cum hæc ſit vna applicatarum in ſectione D E F ad diametrum R N O, qua-
re, & P Q ipſi D E æquidiſtabit, hoc eſt D E erit vna applicatarum in ſe-
ctione A B C ad diametrum R N P; ex quo N E producta ad vtranque par-
tem exteriori ſectioni A B C occurret, vt in L, M, & à diametro P N bifa-
riam ſecabitur in N, ſed D E quoque bifariam ſecta fuit in N, quare inter-
ceptæ L D, E M inter ſe ſunt æquales, hoc eſt rectangulum L D M æquale
eſt rectangulo L E M.

283.1.

43. 44.
huius.
0244-01

Iam cum ſit applicata A C bifariam ſecta in E, ducta eius diametro B
E, hæc quoque bifariam ſecabit aliam applicatam G H, vt in I, eritque
etiam diameter ſectionis parallelæ, vel concentricæ D E F; & cum A C
contingat ſectionem D E F in E, ſitque D F ei æquidiſtans, hæc item bi-
fariam ſecabitur à diametro E I, vt in I. Cum ſit ergo G I æqualis I H, & ablata D I æqualis ablatæ I F, erit reliqua G D reliquæ F H æqualis, ſiue
rectangulum G D H æquale rectangulo G F H.

Tandem ex B ducatur contingens B Q alteri contingenti P Q conue-
niens in Q. Erit ergo rectangulum G D H ad L D M, vt quadratum B Q ad P Q; eademque ratione rectangulum A E C ad L E M, vt quadratum
B Q ad P Q: quapropter rectangulum G D H ad L D M, erit vt A E C ad
L E M, & permutando G D H ad A E C, vel ad quadratum A C, (cum
A E, E C ſint æquales) vt rectangulum L D M ad L E M, ſed L D M ipſi
L E M æquale oſtenſum fuit, quare, & rectangulum G D H, vel G F H
æquale erit quadrato ſemi-tangentis A E. Quod erat demonſtrandum:

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