Elements of Geometry and Trigonometry |
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Page 51
... suppose AB - DE , the angle ACB will be equal to DCE . For , if these angles are not equal , suppose ACB to be the greater , and let ACI be taken equal to DCE . From what has just been shown , we shall have AI = DE : but , by hypothesis ...
... suppose AB - DE , the angle ACB will be equal to DCE . For , if these angles are not equal , suppose ACB to be the greater , and let ACI be taken equal to DCE . From what has just been shown , we shall have AI = DE : but , by hypothesis ...
Page 52
Adrien Marie Legendre Charles Davies. Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is contained 7 ...
Adrien Marie Legendre Charles Davies. Suppose , for example , that the angles ACB , DCE , are to each other as 7 is to 4 ; or , which is the same thing , suppose that the angle M , which may serve as a common measure , is contained 7 ...
Page 54
... suppose that the centre of the cir- cle lies within the angle BAD . Draw the diameter AE , and the radii CB , CD . The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I ...
... suppose that the centre of the cir- cle lies within the angle BAD . Draw the diameter AE , and the radii CB , CD . The angle BCE , being exterior to the triangle ABC , is equal to the sum of the two interior angles CAB , ABC ( Book I ...
Page 63
... suppose them to be drawn ; bisect those two lines by the perpendiculars DE , FG : the point O , where these perpen- diculars meet , will be the centre sought ( Prop . VI . Sch . ) .. Scholium . The same construc- tion serves for making ...
... suppose them to be drawn ; bisect those two lines by the perpendiculars DE , FG : the point O , where these perpen- diculars meet , will be the centre sought ( Prop . VI . Sch . ) .. Scholium . The same construc- tion serves for making ...
Page 66
... Suppose , for instance , we find GB to be contained exactly twice in FD ; BG will be the common measure of the two pro- posed lines . Put BG = 1 ; we shall have FD = 2 : but EB con- tains FD once , plus GB ; therefore we have EB = 3 ...
... Suppose , for instance , we find GB to be contained exactly twice in FD ; BG will be the common measure of the two pro- posed lines . Put BG = 1 ; we shall have FD = 2 : but EB con- tains FD once , plus GB ; therefore we have EB = 3 ...
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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