Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 18
... drawn between two points . 12. The shortest distance between any two points is mea- sured on the straight line which joins them . 13. Through the same point , only one line can be drawn parallel to a given line .. POSTULATES . 1. A ...
... drawn between two points . 12. The shortest distance between any two points is mea- sured on the straight line which joins them . 13. Through the same point , only one line can be drawn parallel to a given line .. POSTULATES . 1. A ...
Page 19
... drawn to a given line , either from a point without , or from a point on the line . 7. A line may be drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point , parallel to a given ...
... drawn to a given line , either from a point without , or from a point on the line . 7. A line may be drawn , making with a given line an angle equal to a given angle . 8. A line may be drawn through a given point , parallel to a given ...
Page 20
... drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles E D A- B ECA and ECB will both be right angles , and conse quently , their sum will be equal to two right angles . The angle DCA is equal to is equal ...
... drawn per- pendicular to AB ( Post . 6 ) ; then , by definition ( D. 12 ) , the angles E D A- B ECA and ECB will both be right angles , and conse quently , their sum will be equal to two right angles . The angle DCA is equal to is equal ...
Page 22
... mutually perpendicular to each other . Cor . 3. The sum of all the angles ACB , BCD , DCE , ECF , FCA , that can be formed about a point , is equal to four right angles . F B 租 For , if two lines be drawn through the point 22 GEOMETRY .
... mutually perpendicular to each other . Cor . 3. The sum of all the angles ACB , BCD , DCE , ECF , FCA , that can be formed about a point , is equal to four right angles . F B 租 For , if two lines be drawn through the point 22 GEOMETRY .
Page 23
... drawn through the point , mutually perpendicular to each other , the sum of the angles which they form will be equal to four right angles , and it will also be equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given ...
... drawn through the point , mutually perpendicular to each other , the sum of the angles which they form will be equal to four right angles , and it will also be equal to the sum of the given angles ( A. 9 ) . Hence , the sum of the given ...
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Common terms and phrases
AB² 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