Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 9
... Spherical Trigonometry John Playfair. PROPOSITION I. THEOREM . If two triangles have two sides and the included angle in the one , equal to two sides and the included angle in the other , the triangles will be identical , or equal in all ...
... Spherical Trigonometry John Playfair. PROPOSITION I. THEOREM . If two triangles have two sides and the included angle in the one , equal to two sides and the included angle in the other , the triangles will be identical , or equal in all ...
Página 15
... Spherical Trigonometry John Playfair. AB ; the angle ABC is also greater than the angle BCA . A D Make AD equal to AB , and join BD : and because ADB is the exterior angle of the triangle BDC , it is greater ( 9. 1. ) than the interior ...
... Spherical Trigonometry John Playfair. AB ; the angle ABC is also greater than the angle BCA . A D Make AD equal to AB , and join BD : and because ADB is the exterior angle of the triangle BDC , it is greater ( 9. 1. ) than the interior ...
Página 18
... Spherical Trigonometry John Playfair. PROP . XVII . THEOR . A perpendicular is the shortest line that can be drawn from a point , situated with- out a straight line , to that line : any two oblique lines drawn from the samę point on ...
... Spherical Trigonometry John Playfair. PROP . XVII . THEOR . A perpendicular is the shortest line that can be drawn from a point , situated with- out a straight line , to that line : any two oblique lines drawn from the samę point on ...
Página 19
... Spherical Trigonometry John Playfair. for the right angles B and E are equal , the side AB = DE , and BH = EF ; hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ; and ...
... Spherical Trigonometry John Playfair. for the right angles B and E are equal , the side AB = DE , and BH = EF ; hence , these tri- angles are equal ( Th . 1. ) , and consequently AH = DF . Now ( by hyp . ) , we have DF - AC ; and ...
Página 26
... Spherical Trigonometry John Playfair. C B D Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal ( 21. 1. ) to one another ; and because AC is parallel to BD , and BC meets them , the alternate ...
... Spherical Trigonometry John Playfair. C B D Because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal ( 21. 1. ) to one another ; and because AC is parallel to BD , and BC meets them , the alternate ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore