Elements of Geometry and Trigonometry |
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Page iii
... propositions of Geometry are general truths , and ought to be stated in general terms , without reference to particular diagrams . In the following work , each proposition is first enunciated in general terms , and afterwards , with ...
... propositions of Geometry are general truths , and ought to be stated in general terms , without reference to particular diagrams . In the following work , each proposition is first enunciated in general terms , and afterwards , with ...
Page 11
... Propositions . 10. A LEMMA is an auxiliary proposition . 11. A COROLLARY is an obvious consequence of one more propositions . or 12. A SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their ...
... Propositions . 10. A LEMMA is an auxiliary proposition . 11. A COROLLARY is an obvious consequence of one more propositions . or 12. A SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their ...
Page 19
... Proposition ; P. for Proposition ; Prob . for Problem ; Post . for Postulate ; and S. for Scholium . In referring to the same Book , the number of the Book is not given ; in referring to any other Book , the number of the Book is given ...
... Proposition ; P. for Proposition ; Prob . for Problem ; Post . for Postulate ; and S. for Scholium . In referring to the same Book , the number of the Book is not given ; in referring to any other Book , the number of the Book is given ...
Page 20
Adrien Marie Legendre Charles Davies. PROPOSITION I. THEOREM . If a straight line meet another straight line , the sum of the adjacent angles will be equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA ...
Adrien Marie Legendre Charles Davies. PROPOSITION I. THEOREM . If a straight line meet another straight line , the sum of the adjacent angles will be equal to two right angles . Let DC meet AB at C : then will the sum of the angles DCA ...
Page 21
... proposition just demonstrated , is equal to two right angles . DEFINITIONS . If two straight lines intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each ...
... proposition just demonstrated , is equal to two right angles . DEFINITIONS . If two straight lines intersect each other , they form four angles about the point of intersection , which have received different names , with respect to each ...
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Elements of Geometry and Trigonometry: From the Works of A. M. Legendre Adrien Marie Legendre,Charles Davies No preview available - 2016 |
Common terms and phrases
AB² ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right-angled triangle Scholium secant segment semi-circumference side BC similar Sine slant height sphere spherical angle spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prisms upper base vertex vertices whence
Popular passages
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 100 - The area of a triangle is equal to half the product of its base by its altitude.
Page 99 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 59 - A chord is a straight line joining the extremities of an arc.
Page 124 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 214 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 43 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 52 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 123 - Similar triangles are to each other as the squares of their homologous sides.
Page 182 - The upper end of the frustum of a pyramid or cone is called the upper base...