Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
From inside the book
Results 1-5 of 32
Page 17
... rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2. A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral ...
... rectangles and rhomboids . 1st . A RECTANGLE is a parallelogram whose angles are all right angles . A SQUARE is an equilateral rectangle . 2. A RHOMBOID is a parallelogram whose angles are all oblique . A RHOMBUS is an equilateral ...
Page 95
... 7 ) ; which was to be proved . Cor . Triangles having equal bases and equal altitudes are equal , for they are halves of equal parallelograms . PROPOSITION III . THEOREM . Rectangles having equal altitudes , BOOK IV . 95.
... 7 ) ; which was to be proved . Cor . Triangles having equal bases and equal altitudes are equal , for they are halves of equal parallelograms . PROPOSITION III . THEOREM . Rectangles having equal altitudes , BOOK IV . 95.
Page 96
... rectangles whose altitudes AD and HK are equal , and whose bases AB and HE are commensurable : then will the areas of the rectangles be proportional to their bases . D K Suppose that AB is to HE , as 7 is to 4. Conceive AB to be divided ...
... rectangles whose altitudes AD and HK are equal , and whose bases AB and HE are commensurable : then will the areas of the rectangles be proportional to their bases . D K Suppose that AB is to HE , as 7 is to 4. Conceive AB to be divided ...
Page 97
... rectangles be incommensurable : then will the rectangles be proportional to their bases . For , place the rectangle HEFK upon the rectangle ABCD , so that it shall take the position AEFD . Then , if the rectangles are not pro- portional ...
... rectangles be incommensurable : then will the rectangles be proportional to their bases . For , place the rectangle HEFK upon the rectangle ABCD , so that it shall take the position AEFD . Then , if the rectangles are not pro- portional ...
Page 98
... rectangles are to each other as the products of their bases and altitudes . H D Let ABCD and AEGF be two rectangles ... rectangle AEGF will be the superficial unit , and we shall have , ABCD : 1 :: AB × AD 1 ; ABCD AB × AD : hence , the ...
... rectangles are to each other as the products of their bases and altitudes . H D Let ABCD and AEGF be two rectangles ... rectangle AEGF will be the superficial unit , and we shall have , ABCD : 1 :: AB × AD 1 ; ABCD AB × AD : hence , the ...
Other editions - View all
Common terms and phrases
AB² ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following