Elements of Geometry and Trigonometry |
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Page 3
... denote a limited portion of space , seems cal- culated to introduce the foreign idea of matter into a science , which deals only with the abstract properties and relations of figured space . The term volume , has been introduced in its ...
... denote a limited portion of space , seems cal- culated to introduce the foreign idea of matter into a science , which deals only with the abstract properties and relations of figured space . The term volume , has been introduced in its ...
Page 55
... denote their ratio . B will A If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B MA A = whence , mA : mB :: A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four ...
... denote their ratio . B will A If we multiply both terms of this fraction by m , its value will not be changed ; and we shall have , mB B MA A = whence , mA : mB :: A : B ; which was to be proved . PROPOSITION VIII . THEOREM . If four ...
Page 86
... denote the given sides , and A the give angle . Draw the indefinite line DF and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the gide C , and on DE , lay off DG equal to the side B ; draw E H.F D B C ...
... denote the given sides , and A the give angle . Draw the indefinite line DF and at D construct an angle FDE , equal to the angle A ; on DF , lay off DH equal to the gide C , and on DE , lay off DG equal to the side B ; draw E H.F D B C ...
Page 147
... at I and Prolong 40 to E. be perpendicular to it . Let P denote the circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we shall have ( P. IX . ) , Pp :: ᎾᏦ or OA ' : OI ; hence BOOK V. 147.
... at I and Prolong 40 to E. be perpendicular to it . Let P denote the circumscribed , and p the inscribed polygon ; then , because they are regular and similar , we shall have ( P. IX . ) , Pp :: ᎾᏦ or OA ' : OI ; hence BOOK V. 147.
Page 148
... denotes their difference and a quantity greater than their differ- ence , at the same time , which is impossible ; therefore , the two quantities are ultimately equal . * Newton's Principia , Book I. , Lemma I. • Cor . If we take any ...
... denotes their difference and a quantity greater than their differ- ence , at the same time , which is impossible ; therefore , the two quantities are ultimately equal . * Newton's Principia , Book I. , Lemma I. • Cor . If we take any ...
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Common terms and phrases
ABCD ACē adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence