4523
[Commentary:
This page contains further work on Viète's statement of 'Syntomon' in Chapter XIX, Proposition 21, Variorum responsorum liber VIII
(Viete 1593d, Chapter 19, Prop .
Quæ per factionem sub sinibus peripheriarum & adplicationem ad sinum totum exurgunt, eadem opere additionis vel subductionis præsto sunt.
Cum duæ peripheriæ angulum acutum componunt, est
Vt sinus totus ad sinum duplum primæ, ita sinus secundæ ad sinum complementi differentia, minus sinu complementi composita.
What appears from a combination of the sine of the arcs, dividing the sine of the total, is also shown by the operations of addition and subtraction.
When two arcs contain acute angles, then as the whole sine is to twice the sine of the first, so is the sine of the second to the sum of the sine of the complement of the difference minus the sine of the complement of the ]
Quæ per factionem sub sinibus peripheriarum & adplicationem ad sinum totum exurgunt, eadem opere additionis vel subductionis præsto sunt.
Cum duæ peripheriæ angulum acutum componunt, est
Vt sinus totus ad sinum duplum primæ, ita sinus secundæ ad sinum complementi differentia, minus sinu complementi composita.
What appears from a combination of the sine of the arcs, dividing the sine of the total, is also shown by the operations of addition and subtraction.
When two arcs contain acute angles, then as the whole sine is to twice the sine of the first, so is the sine of the second to the sum of the sine of the complement of the difference minus the sine of the complement of the ]
De 3o et 4o ton syntomon
[Translation: On cases 3 and 4 of ]
[Translation: On cases 3 and 4 of ]
Etsi duo priores casus
sufficiunt ad operationes:
duo tamen sequentes ad
argumentationes sunt ali-
quando
[Translation: Although the two first cases suffice for working, nevertheless the two following arguments are sometimes necessary.
sufficiunt ad operationes:
duo tamen sequentes ad
argumentationes sunt ali-
quando
[Translation: Although the two first cases suffice for working, nevertheless the two following arguments are sometimes necessary.
3us casus est, quando unus
datorum arcuum sit maior
quadrante; et differentia sit
etiam quadrante
[Translation: The 3rd case is when one of the given arcs is greater than a quadrant, and the difference is also greater than a ]
datorum arcuum sit maior
quadrante; et differentia sit
etiam quadrante
[Translation: The 3rd case is when one of the given arcs is greater than a quadrant, and the difference is also greater than a ]
4us casus est, quando unus datorum
arcuum sit maior quadrante;
sed differentia sit quadrante
[Translation: The 4th case is when one of the given arcs is greater than a quadrant, but the difference is ]
arcuum sit maior quadrante;
sed differentia sit quadrante
[Translation: The 4th case is when one of the given arcs is greater than a quadrant, but the difference is ]