Elements of Geometry and Trigonometry |
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Page 16
... Let the triangle EDF , be placed upon the triangle BAC , so that the point E shall fall upon B , and the side ED on the equal side BA ; then , since the angle D is equal to the angle A , the side DF will take the direction AC . But DF ...
... Let the triangle EDF , be placed upon the triangle BAC , so that the point E shall fall upon B , and the side ED on the equal side BA ; then , since the angle D is equal to the angle A , the side DF will take the direction AC . But DF ...
Page 17
... Let the angle E be equal to the angle B , the angle F to the angle C , and ... falling on B , and the point F on C ; then , since the angle E is equal to the angle B ... fall at their intersection A : hence , the two triangles EDF , BAC ...
... Let the angle E be equal to the angle B , the angle F to the angle C , and ... falling on B , and the point F on C ; then , since the angle E is equal to the angle B ... fall at their intersection A : hence , the two triangles EDF , BAC ...
Page 19
... fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . Да B Third Case . Lastly , if the point G fall ... Let the side ED = BA , the side EF BOOK I. 19.
... fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . Да B Third Case . Lastly , if the point G fall ... Let the side ED = BA , the side EF BOOK I. 19.
Page 22
... let fall on the line , and oblique lines be drawn to different points : · 1st , The perpendicular will be shorter than any oblique line . 2d , Any two oblique lines , drawn on different sides of the perpen- dicular , cutting off equal ...
... let fall on the line , and oblique lines be drawn to different points : · 1st , The perpendicular will be shorter than any oblique line . 2d , Any two oblique lines , drawn on different sides of the perpen- dicular , cutting off equal ...
Page 25
... Let the two lines AC , BD , A be perpendicular to AB ; then will they be parallel , For , if they could meet in a point O , on either side of AB , there would be two per- B C D pendiculars OA , OB , let fall from the same point on the ...
... Let the two lines AC , BD , A be perpendicular to AB ; then will they be parallel , For , if they could meet in a point O , on either side of AB , there would be two per- B C D pendiculars OA , OB , let fall from the same point on the ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex