Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
From inside the book
Results 6-10 of 40
Page 41
... four acute angles are equal , and so , also , are the four obtuse angles . PROPOSITION XXI . THEOREM . If two straight lines intersect a third line , making the sum of the interior angles on the same side less than two right angles ...
... four acute angles are equal , and so , also , are the four obtuse angles . PROPOSITION XXI . THEOREM . If two straight lines intersect a third line , making the sum of the interior angles on the same side less than two right angles ...
Page 46
... four , divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the sides of the polygon ABCDE be prolonged , in the same order , forming the ...
... four , divided by the number of angles . PROPOSITION XXVII . THEOREM . The sum of the exterior angles of a polygon is equal to four right angles . Let the sides of the polygon ABCDE be prolonged , in the same order , forming the ...
Page 47
... four right angles ; which was to be proved . PROPOSITION XXVIII . THEOREM . In any parallelogram , the opposite sides are equal , each to each . Let ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D For , draw the ...
... four right angles ; which was to be proved . PROPOSITION XXVIII . THEOREM . In any parallelogram , the opposite sides are equal , each to each . Let ABCD be a parallelogram : then will AB be equal to DC , and AD to BC . D For , draw the ...
Page 50
... : HI , & c . 4. There are four terms in every proportion . The first and second form the first couplet , and the third and fourth , the second couplet . The first and fourth terms are BOOK II Ratios and Proportions, BOOK III.
... : HI , & c . 4. There are four terms in every proportion . The first and second form the first couplet , and the third and fourth , the second couplet . The first and fourth terms are BOOK II Ratios and Proportions, BOOK III.
Page 51
... Equimultiples of two or more quantities , are the pro- Jucts obtained by multiplying both by the same quantity . Thus , mA and mB , are equimultiples of A and B. PROPOSITION I THEOREM . If four quantities are in proportion BOOK II . 51.
... Equimultiples of two or more quantities , are the pro- Jucts obtained by multiplying both by the same quantity . Thus , mA and mB , are equimultiples of A and B. PROPOSITION I THEOREM . If four quantities are in proportion BOOK II . 51.
Other editions - View all
Common terms and phrases
AB² AC² altitude angle ACB apothem axis base and altitude base multiplied BC² bisect centre chord circumference coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diameter distance divided draw drawn edges equal bases equal in volume equal to AC equal to half equally distant Formula frustum given angle given line greater hence homologous hypothenuse included angle intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides opposite parallelogram perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION XI proved pyramid quadrant radii radius rectangle regular polygons right-angled triangle Scholium segment semi-circumference side BC similar sine slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence