Elements of Geometry and Trigonometry: From the Works of A.M. Legendre |
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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 or more propositions . 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 or more propositions . 12. A SCHOLIUM is a remark made upon one or more propositions , with reference to their connection , their ...
Page 19
... 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 I ...
... 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 I ...
Page 20
From the Works of A.M. Legendre Adrien Marie Legendre. 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 ...
From the Works of A.M. Legendre Adrien Marie Legendre. 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 ...
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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Common terms and phrases
ABē ABCD ACē adjacent angles altitude 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 difference distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa 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 polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine slant height sphere spherical polygon spherical triangle square subtracted Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence
Popular passages
Page 126 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 59 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Page 18 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, and each degree into 60 equal parts called minutes, and each minute into 60 equal parts called seconds, and these into thirds, fourths, &c.
Page 104 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 6 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 28 - If two triangles have two sides of the one equal to two sides of the...
Page 46 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 99 - The area of a parallelogram is equal to the product of its base and altitude.
Page 172 - If two planes are perpendicular to 'each other, a straight line drawn in one of them, perpendicular to their intersection, will be perpendicular to the other.
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.