Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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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 12
... proposition , or in the course of a demonstra- tion . 14. Two magnitudes are equal , when they are equal in measure . When they may be so placed as to coincide through . out their whole extent , they are equal in all their parts ...
... proposition , or in the course of a demonstra- tion . 14. Two magnitudes are equal , when they are equal in measure . When they may be so placed as to coincide through . out their whole extent , they are equal in all their parts ...
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 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 ...
Page 22
... proposition is proved . Cor . 1. If one of the angles about all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle will also be a ...
... proposition is proved . Cor . 1. If one of the angles about all of the others will be right angles also . each of its adjacent angles will be a right angle ; and from the proposition just demonstrated , its opposite angle will also be a ...
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Common terms and phrases
ABē 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