Elements of Geometry and Trigonometry |
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Page 71
Adrien Marie Legendre Charles Davies. Let ABCD , AEFD , be two rectan D gles having the common altitude AD : they are to each other as their bases AB , AE . E Suppose , first , that the bases are A commensurable , and are to each other ...
Adrien Marie Legendre Charles Davies. Let ABCD , AEFD , be two rectan D gles having the common altitude AD : they are to each other as their bases AB , AE . E Suppose , first , that the bases are A commensurable , and are to each other ...
Page 80
... gles ABD , ADC , give AD2 + BD2 = AB2 , and AD2 + CD2 AC2 , we have AB2 = BC2 + AC2-2BC x CD . Secondly . When the perpendicular AD falls without the triangle ABC , we have BD -CD - BC ; and consequently BD2 ÷ CD2 + BC2—2CD × BC ( Prop ...
... gles ABD , ADC , give AD2 + BD2 = AB2 , and AD2 + CD2 AC2 , we have AB2 = BC2 + AC2-2BC x CD . Secondly . When the perpendicular AD falls without the triangle ABC , we have BD -CD - BC ; and consequently BD2 ÷ CD2 + BC2—2CD × BC ( Prop ...
Page 86
... gles will be similar . Take AG - DE , and draw GH paral- lel to BC . The angle AGH will be equal to the angle ABC ( Book I. Prop . XX . A D E I Cor 3. ) ; and the triangles AGH , ABC , will be equiangular : hence we shall have AB : AG ...
... gles will be similar . Take AG - DE , and draw GH paral- lel to BC . The angle AGH will be equal to the angle ABC ( Book I. Prop . XX . A D E I Cor 3. ) ; and the triangles AGH , ABC , will be equiangular : hence we shall have AB : AG ...
Page 89
... gles DAC and BAC are similar ; hence all the triangles are equiangular and similar . Secondly . The triangles BAD , BAC , being similar , their homologous sides are proportional . But BD in the small tri- angle , and BA in the large one ...
... gles DAC and BAC are similar ; hence all the triangles are equiangular and similar . Secondly . The triangles BAD , BAC , being similar , their homologous sides are proportional . But BD in the small tri- angle , and BA in the large one ...
Page 91
... gles , having the angle A equal to D , and the angle B = E . . · Then , first , by reason of the equal an- gles A and D , according to the last pro- position , we shall have ABC DEF :: AB.AC : DE.DF. Also , because the triangles are ...
... gles , having the angle A equal to D , and the angle B = E . . · Then , first , by reason of the equal an- gles A and D , according to the last pro- position , we shall have ABC DEF :: AB.AC : DE.DF. Also , because the triangles are ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex