Elements of Geometry and Trigonometry |
From inside the book
Results 1-5 of 42
Page 11
... rectangle , which has its angles right an- gles , without having its sides equal . The parallelogram , or rhomboid , which has its opposite sides parallel . The rhombus , or lozenge , which has its sides equal , without having its ...
... rectangle , which has its angles right an- gles , without having its sides equal . The parallelogram , or rhomboid , which has its opposite sides parallel . The rhombus , or lozenge , which has its sides equal , without having its ...
Page 31
... rectangle and the square . Cor . 2. The sum of the angles of a pentagon is equal to two right angles multiplied by 5-2 , which amounts to six right angles : hence , when a pentagon is equiangular , each angle is equal to the fifth part ...
... rectangle and the square . Cor . 2. The sum of the angles of a pentagon is equal to two right angles multiplied by 5-2 , which amounts to six right angles : hence , when a pentagon is equiangular , each angle is equal to the fifth part ...
Page 70
... rectangle ABGH , which has the same base AB , and the same altitude AH : for the rectangle ABGH is equivalent to the parallelogram ABCD ( Prop . I. Cor . ) . Cor . 2. All triangles , which have equal bases and altitudes , are equivalent ...
... rectangle ABGH , which has the same base AB , and the same altitude AH : for the rectangle ABGH is equivalent to the parallelogram ABCD ( Prop . I. Cor . ) . Cor . 2. All triangles , which have equal bases and altitudes , are equivalent ...
Page 71
... rectangle ABCD will contain seven partial rectangles , while AEFD will contain four : hence the rectangle ABCD is to AEFD as 7 is to 4 , or as AB is to AE . The same reasoning may be applied to any other ratio equally with that of 7 to ...
... rectangle ABCD will contain seven partial rectangles , while AEFD will contain four : hence the rectangle ABCD is to AEFD as 7 is to 4 , or as AB is to AE . The same reasoning may be applied to any other ratio equally with that of 7 to ...
Page 72
... rectangle , provided we under- stand by this product , the product of two numbers , one of which is the number of linear units contained in the base , the other the number of linear units contained in the altitude . This product will ...
... rectangle , provided we under- stand by this product , the product of two numbers , one of which is the number of linear units contained in the base , the other the number of linear units contained in the altitude . This product will ...
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.