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
... fall on C , and the third side EF , will coincide with the third side BC ( Ax . 11. ) : therefore , the triangle EDF ... Let the angle E be equal to the angle B , the angle F to the angle C , and the in- Icluded side EF to the in- cluded side ...
... fall on C , and the third side EF , will coincide with the third side BC ( Ax . 11. ) : therefore , the triangle EDF ... Let the angle E be equal to the angle B , the angle F to the angle C , and the in- Icluded side EF to the in- cluded side ...
Page 19
... fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B Third Case . Lastly , if the point G fall ... Let the side ED = BA , the side EF · BOOK 1 . 19.
... fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC ( Ax . 8. ) . B Third Case . Lastly , if the point G fall ... Let the side ED = BA , the side EF · BOOK 1 . 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 C , on either side of AB , there would be two per- B 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 C , on either side of AB , there would be two per- B D pendiculars OA , OB , let fall from the same point on the ...
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface Cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles 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 parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular 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 slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex
Popular passages
Page 241 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 19 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 232 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 168 - The radius of a sphere is a straight line drawn from the centre to any point of the surface ; the diameter or axis is a line passing through this centre, and terminated on both sides by the surface.
Page 18 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 169 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude, Fig.
Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 86 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 225 - B) = cos A cos B — sin A sin B, (6a) cos (A — B) = cos A cos B + sin A sin B...
Page 168 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.