Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 41
Page 6
... Triangles , 257 Solution of Oblique angled Triangles by Logarithms , · 259 MENSURATION . Mensuration of Surfaces , Mensuration of Solids . · 274 285 AN INDEX SHOWING THE PROPOSITIONS OF LEGENDRE WHICH CORRESPOND TO vi CONTENTS .
... Triangles , 257 Solution of Oblique angled Triangles by Logarithms , · 259 MENSURATION . Mensuration of Surfaces , Mensuration of Solids . · 274 285 AN INDEX SHOWING THE PROPOSITIONS OF LEGENDRE WHICH CORRESPOND TO vi CONTENTS .
Page 7
Adrien Marie Legendre Charles Davies. AN INDEX SHOWING THE PROPOSITIONS OF LEGENDRE WHICH CORRESPOND TO THE PRINCIPAL PROPOSITIONS OF THE FIRST SIX BOOKS OF EUCLID . Euclid . Legendre . Euclid . Legendre . Euclid . Legendre . Book I ...
Adrien Marie Legendre Charles Davies. AN INDEX SHOWING THE PROPOSITIONS OF LEGENDRE WHICH CORRESPOND TO THE PRINCIPAL PROPOSITIONS OF THE FIRST SIX BOOKS OF EUCLID . Euclid . Legendre . Euclid . Legendre . Euclid . Legendre . Book I ...
Page 12
... corresponding signification , with respect to the angles . In both cases , the equal sides , or the equal angles , are named homologous sides or angles . Definitions of terms employed in Geometry . An axiom is a self - evident ...
... corresponding signification , with respect to the angles . In both cases , the equal sides , or the equal angles , are named homologous sides or angles . Definitions of terms employed in Geometry . An axiom is a self - evident ...
Page 32
... and the figure be a par- allelogram . A D C B For , having drawn the diagonal BD , the triangles ABD , BDC , have all the sides of the one equal to the corresponding sides of the other ; therefore they are 32 GEOMETRY .
... and the figure be a par- allelogram . A D C B For , having drawn the diagonal BD , the triangles ABD , BDC , have all the sides of the one equal to the corresponding sides of the other ; therefore they are 32 GEOMETRY .
Page 33
... corresponding sides of the other , and are therefore equal : whence it follows that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . BOOK II . OF RATIOS AND ...
... corresponding sides of the other , and are therefore equal : whence it follows that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . BOOK II . OF RATIOS AND ...
Other editions - View all
Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface cosine Cotang 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 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 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 11 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
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 31 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon...
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 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 159 - S-ahc be the smaller : and suppose Aa to be the altitude of a prism, which having ABC for its base, is equal to their difference. Divide the altitude AT into equal parts Ax, xy, yz, &c. each less than Aa, and let k be one of those parts ; through the points of division...
Page 64 - To inscribe a circle in a given triangle. Let ABC be the given triangle. Bisect the angles A and B by the lines AO and BO, meeting at the point 0.