Elements of Geometry and Trigonometry |
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Page 12
... theorem , or the solution of a problem . The common name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions . A scholium is a ...
... theorem , or the solution of a problem . The common name , proposition , is applied indifferently , to theorems , problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions . A scholium is a ...
Page 13
... drawn which shall be parallel to a given line . 13. Magnitudes , which being applied to each other , coincide throughout their whole extent , are equal . B PROPOSITION I. THEOREM . If one straight line meet another BOOK I. 13.
... drawn which shall be parallel to a given line . 13. Magnitudes , which being applied to each other , coincide throughout their whole extent , are equal . B PROPOSITION I. THEOREM . If one straight line meet another BOOK I. 13.
Page 14
... THEOREM . Two straight lines , which have two points common , coincide with each other throughout their whole extent , and form one ana the same straight line . Let A and B be the two common points . In the first place it is evident ...
... THEOREM . Two straight lines , which have two points common , coincide with each other throughout their whole extent , and form one ana the same straight line . Let A and B be the two common points . In the first place it is evident ...
Page 15
... THEOREM . If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to two right angles , the two straight lines which are met , will form one and the same straight line . Let ...
... THEOREM . If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to two right angles , the two straight lines which are met , will form one and the same straight line . Let ...
Page 18
... THEOREM . The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short ...
... THEOREM . The sum of any two sides of a triangle , is greater than the third side . Let ABC be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For the straight line AB is the short ...
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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 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.