. Trigonometria. rectangle of AH and HEis cquai to the rectangle of 7 A E and CF , which was to beproved. Confettitry. Therefore the fine of the fimple anddouble arches being g{ven,the fine complement of thefimple arch is alfo given. For as EH the fine of rhe fimple arch- is to the half of Radius; fois CF the fine of the double arch to H A the fine complement of H E. j 8 The co-fine of the half fum of two arches together leffe then a Semii irele, is to the dif-ference of the fines, as the half Radius is to the fine of half the difference. Demiti(ha*. Let the given arches (/»the following Daara
. Trigonometria. rectangle of AH and HEis cquai to the rectangle of 7 A E and CF , which was to beproved. Confettitry. Therefore the fine of the fimple anddouble arches being g{ven,the fine complement of thefimple arch is alfo given. For as EH the fine of rhe fimple arch- is to the half of Radius; fois CF the fine of the double arch to H A the fine complement of H E. j 8 The co-fine of the half fum of two arches together leffe then a Semii irele, is to the dif-ference of the fines, as the half Radius is to the fine of half the difference. Demiti(ha*. Let the given arches (/»the following Daaram) be D F and F E, their fines areDM and EN, and D L is the difference of thofe fines, E F H is the (umme of the given ar-ches, and D E their difference ; Now then in thetriangle D L E, as . Rad. D E:: s E. D L, and therefore alfo, ~ Rad. 7 D £ :: s £. D L, the differenceof the fines. H Tht. the rickand AB Ingonomeiria BrkmnkA e 19 The right fines of the half fum and half difference of two arches are mean proportionalsbetween the whole Sine and the half difference of the verfed fines. Demonftration. C Let the given arches be D F and F E, and their verfedfines M F and F N, their difference is M N, equal to L Eand EF H is the fumme ot the arches given, D E theirdifference : Now then in the Triangle D L E, it isas Rad. DE :: Andalfo,Rad.|DE::; 10 The fine of the fumme of two arches togetherlefle then a Semicircle, is to the difference of the Sines;as the fine of the half fumme is to the fine of the halfdifference. Demonftration. In the Circle A D E, let the given arches be D E and D C, and letlines CK and DF be perpendicular to the diameter A E, and the arches EO, to D C, then are the triangles E C K. and H D Glike, becaufe of their parallel fides E C and H D, andtheir right angles at G and K, then is CK the fine ofthe fumme, and D G the difference of t
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Keywords: ., bookcentury1600, bookdecade1650, bookidtrigonometri, bookyear1658
