Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 77
... quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is ...
... quadrant , is taken as a unit . If , therefore , any angle be measured by one - half or two - thirds of a quadrant , it will be equal to one - half or two - thirds of a right angle . PROPOSITION XVIII . THEOREM . An inscribed angle is ...
Page 79
... quadrant ( P. XVII . , S. ) . Cor . 3. Any angle BAC , in- scribed in a segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi - circumference . Any angle BOC , inscribed in a ...
... quadrant ( P. XVII . , S. ) . Cor . 3. Any angle BAC , in- scribed in a segment greater than a semi - circle , is acute ; for it is mea- sured by half the arc BOC , less than a semi - circumference . Any angle BOC , inscribed in a ...
Page 242
... quadrant ; the point C being the pole of the arc DE , the distance CE , is likewise a quadrant : hence , the point E is at a quadrant's distance from the points A and C : hence , it is the pole of the arc AC ( P. III . , C. 4 ) . It may ...
... quadrant ; the point C being the pole of the arc DE , the distance CE , is likewise a quadrant : hence , the point E is at a quadrant's distance from the points A and C : hence , it is the pole of the arc AC ( P. III . , C. 4 ) . It may ...
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... four equal parts , called quadrants ; and because each of the angles at the cen- tre is a right angle , it follows that a right angle is measured by a quad- D rant . Au acute angle is measured by an arc PLANE TRIGONOMETRY.
... four equal parts , called quadrants ; and because each of the angles at the cen- tre is a right angle , it follows that a right angle is measured by a quad- D rant . Au acute angle is measured by an arc PLANE TRIGONOMETRY.
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... QUADRANTS . 63. Let α denote any arc less than 90 ° . has preceded , we know that , From what sin ( 90 ° - a ) = cos a ; cos ( 90 ° — a ) - = sin a . tan ( 90 ° ― a ) = cot a ; cot ( 90 ° - a ) = tan a . sec ( 90 ° - a ) = cosec a ...
... QUADRANTS . 63. Let α denote any arc less than 90 ° . has preceded , we know that , From what sin ( 90 ° - a ) = cos a ; cos ( 90 ° — a ) - = sin a . tan ( 90 ° ― a ) = cot a ; cot ( 90 ° - a ) = tan a . sec ( 90 ° - a ) = cosec a ...
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Common terms and phrases
AB² AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given straight line greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin lower base mantissa mean proportional measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment semi-circumference side BC similar sine six right slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence