Elements of Geometry and Trigonometry |
From inside the book
Results 6-10 of 27
Page 68
... parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases , Thus , EF is the altitude of the parallelo- A gram DB . 7. The altitude of a trapezoid is the per- pendicular drawn between its ...
... parallelogram is the perpendicular which measures the distance between two opposite sides taken as bases , Thus , EF is the altitude of the parallelo- A gram DB . 7. The altitude of a trapezoid is the per- pendicular drawn between its ...
Page 69
... Parallelograms which have equal bases and equal altitudes , are equivalent . D CF EDF CE X Let AB be the common base of the two parallelograms ABCD ... parallelogram ABCD . Hence these two parallelograms ABCD , ABEF , which have BOOK IV . 69.
... Parallelograms which have equal bases and equal altitudes , are equivalent . D CF EDF CE X Let AB be the common base of the two parallelograms ABCD ... parallelogram ABCD . Hence these two parallelograms ABCD , ABEF , which have BOOK IV . 69.
Page 70
... parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same base and the same altitude . EH D G C F A B Let ABCD be ...
... parallelogram is equivalent to the rectangle which has the same base and the same altitude . PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same base and the same altitude . EH D G C F A B Let ABCD be ...
Page 73
... square constructed on a double line is evidently four times greater than the square on a single one ; on a triple line it is nine times great- er , & c . 10 . G PROPOSITION V. THEOREM . The area of any parallelogram is BOOK IV . 73.
... square constructed on a double line is evidently four times greater than the square on a single one ; on a triple line it is nine times great- er , & c . 10 . G PROPOSITION V. THEOREM . The area of any parallelogram is BOOK IV . 73.
Page 74
... parallelogram ABCD . E C B Cor . Parallelograms of the same base are to each other as their altitudes ; and parallelograms of the same altitude are to each other as their bases : for , let B be the common base , and C and D the ...
... parallelogram ABCD . E C B Cor . Parallelograms of the same base are to each other as their altitudes ; and parallelograms of the same altitude are to each other as their bases : for , let B be the common base , and C and D the ...
Other editions - View all
Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex