Elements of Geometry and Trigonometry |
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Page 22
... dicular , cutting off equal distances on the other line , will be equal . 3d , Of two oblique lines , drawn at pleasure , that which is farther from the perpendicular will be the longer . Let A be the given point , DE the given 22 ...
... dicular , cutting off equal distances on the other line , will be equal . 3d , Of two oblique lines , drawn at pleasure , that which is farther from the perpendicular will be the longer . Let A be the given point , DE the given 22 ...
Page 24
... dicular , and therefore equal ( Prop . XV . ) . So , kewise , are the two oblique lines AE , EB , the A two AF , FB , and so on . Therefore every point in the perpendicular is equally distant from the extremities A and B. F E H Secondly ...
... dicular , and therefore equal ( Prop . XV . ) . So , kewise , are the two oblique lines AE , EB , the A two AF , FB , and so on . Therefore every point in the perpendicular is equally distant from the extremities A and B. F E H Secondly ...
Page 28
... dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . R Q D P B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD ...
... dicular to CD . Hence AB and CD are . perpendicular to the same straight line ; hence they are parallel ( Prop . XVIII . ) . R Q D P B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD ...
Page 46
... dicular FG , it is also equally distant from the two points B and C : hence the three distances OA , OB , OC , are equal ; there- fore the circumference described from the centre O , with the radius OB , will pass through the three ...
... dicular FG , it is also equally distant from the two points B and C : hence the three distances OA , OB , OC , are equal ; there- fore the circumference described from the centre O , with the radius OB , will pass through the three ...
Page 58
... dicular on this line . Let A be the point , and BD the straight line . From the point A as a centre , and with a radius sufficiently great , describe an arc cutting the line BD in the two points B and D ; then mark a point E , equally ...
... dicular on this line . Let A be the point , and BD the straight line . From the point A as a centre , and with a radius sufficiently great , describe an arc cutting the line BD in the two points B and D ; then mark a point E , equally ...
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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.