. Trigonometria. And multiplying the former part of this proporti-on, by the difference of the fines of the angles, andthe latter part thereof, by the tangent of half the dif-ference of the fides A B, and A Ey it will be, As the fquare of the difference of the fines of Band E, Is to the reUangle made of the fummt and difference of thefines of B and E : Soisthe fquare of the tangent of the half diffe-rence of B A, and A E, To the rectangle made of the tangents of the half fumme, and half difference of the fides. But by the firft Section, As the fquare of the fine of the fumme of B and E ;Is to
. Trigonometria. And multiplying the former part of this proporti-on, by the difference of the fines of the angles, andthe latter part thereof, by the tangent of half the dif-ference of the fides A B, and A Ey it will be, As the fquare of the difference of the fines of Band E, Is to the reUangle made of the fummt and difference of thefines of B and E : Soisthe fquare of the tangent of the half diffe-rence of B A, and A E, To the rectangle made of the tangents of the half fumme, and half difference of the fides. But by the firft Section, As the fquare of the fine of the fumme of B and E ;Is to the reUangle made of the fumme and difference of the fines ; So is the fquare of the tangent half B E;To the reti angle made of the tangent bMf fumme, and half difference of the (ides. Therefore,As the fquare of the fine of the fumme of B and E,Is to the fquare of the difference of the fines of B and E; So is the fquare of the tangent half B E,Tothc fqiiaic of the tangent of half the difference of the fides. And. vK, Trigonometria Eritannica. 69 And alfo , As the fine of the fumme of the angles B and E ; Is to the difference ofthei lints; So is the tangent ofhalfe the bafe B E , To the tangent of half the difference of the fides B A> and A E. But, As the fine of the half fumme of B and E; Is to the fine of their half difference ;So is the fine of the fumme,to the difference of the fines. And therefore As the fine of the half fumme of the angles B and E jIs to the fine of the half difference of B and E : So is the tangent of half B E,To the tangent of half the difference of the fides B A, and AE; which is the firft part ofthe Propofition. Section 3» Having in the laft Section already proved, by the 3 Confe£t of the 2 Axiom hereof; • That the fumme of the fines of the angles B and E, Is to the differ, of the fines of thofe angks;As the tangent of the half fumme of the fides, Is to the tangent of their half difference. Therefore, if you multiply the fo
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