Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 37
... principle just demonstrated . EXAMPLES . 1. Given B = 58 ° 07 ' , C = 22 ° 37 ' , and a = 408 , tr find A , b , and c . OPERATION . B C A · • • · 58 ° 07 ' 22 ° 37 ' • · 180 ° 80 ° 44 ' 99 ° 16 ' . • - To find b , write the proportion ...
... principle just demonstrated . EXAMPLES . 1. Given B = 58 ° 07 ' , C = 22 ° 37 ' , and a = 408 , tr find A , b , and c . OPERATION . B C A · • • · 58 ° 07 ' 22 ° 37 ' • · 180 ° 80 ° 44 ' 99 ° 16 ' . • - To find b , write the proportion ...
Page 43
... principle : • · ( 14. ) In any plane triangle , the sum of the sides including either angle , is to their difference ... principle just demonstrated . Knowing the half sum and the half difference , the greater angle is found by adding ...
... principle : • · ( 14. ) In any plane triangle , the sum of the sides including either angle , is to their difference ... principle just demonstrated . Knowing the half sum and the half difference , the greater angle is found by adding ...
Page 106
... principle demonstrated in Prop . V. , we have the following RULE . in Book IV . , Multiply the base by the altitude ; the product will be the area required . EXAMPLES . 1. Find the area of a parallelogram , whose base is 12.25 , and ...
... principle demonstrated in Prop . V. , we have the following RULE . in Book IV . , Multiply the base by the altitude ; the product will be the area required . EXAMPLES . 1. Find the area of a parallelogram , whose base is 12.25 , and ...
Page 107
From the Works of A. M. Legendre Adrien Marie Legendre. 0 From the principle demonstrated in Book X , Prop . VI . , we may write the following RULE . Multiply the base by half the altitude ; the product will be the area required . EXAMPLES ...
From the Works of A. M. Legendre Adrien Marie Legendre. 0 From the principle demonstrated in Book X , Prop . VI . , we may write the following RULE . Multiply the base by half the altitude ; the product will be the area required . EXAMPLES ...
Page 110
... principle demonstrated in B the last case , we have , A4 C Q = bc sin A. But , from Formula ( A ' ) , Trig 110 MENSURATION.
... principle demonstrated in B the last case , we have , A4 C Q = bc sin A. But , from Formula ( A ' ) , Trig 110 MENSURATION.
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Common terms and phrases
AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following