Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Elements of Plane and Spherical TrigonometryLippincott, Grambo & Company, 1854 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 13.
Σελίδα 41
... hypotenuse diminished by the square of the other side ; which is thus expressed : AB2 - BC - AC2 . COR . 2. If AB = AC ; that is , if the triangle ABC be right angled and isosceles ; BC2 = 2AB2 = 2AC2 ; therefore , BC = AB√2 . COR . 3 ...
... hypotenuse diminished by the square of the other side ; which is thus expressed : AB2 - BC - AC2 . COR . 2. If AB = AC ; that is , if the triangle ABC be right angled and isosceles ; BC2 = 2AB2 = 2AC2 ; therefore , BC = AB√2 . COR . 3 ...
Σελίδα 42
... hypotenuse and one side of a right angled triangle , are respective- ly equal to the hypotenuse and one side of another ; the two right angled triangles are equal . Suppose the hypotenuse AC - DF , and the side AB - DE ; the right ...
... hypotenuse and one side of a right angled triangle , are respective- ly equal to the hypotenuse and one side of another ; the two right angled triangles are equal . Suppose the hypotenuse AC - DF , and the side AB - DE ; the right ...
Σελίδα 45
... hypotenuse would meet BC at equal distances from the common perpendicular , these triangles would be equal . Secondly . If the given angle be acute , and the side opposite to it greater than the adjacent side , the same mode of ...
... hypotenuse would meet BC at equal distances from the common perpendicular , these triangles would be equal . Secondly . If the given angle be acute , and the side opposite to it greater than the adjacent side , the same mode of ...
Σελίδα 85
... hypotenuse common to two equal right angled triangles . B D F E A A D PROP . XXXVII . THEOR . B E F C If from a point without a circle there be drawn two straight lines , one of which cuts the circle , and the other meets it ; if the ...
... hypotenuse common to two equal right angled triangles . B D F E A A D PROP . XXXVII . THEOR . B E F C If from a point without a circle there be drawn two straight lines , one of which cuts the circle , and the other meets it ; if the ...
Σελίδα 220
... hypotenuse to either of the sides , so the radius to the sine of the angle opposite to that side ; and as either of the sides is to the other side , so is the radius to the tangent of the angle oppo- site to that side . Let ABC be a ...
... hypotenuse to either of the sides , so the radius to the sine of the angle opposite to that side ; and as either of the sides is to the other side , so is the radius to the tangent of the angle oppo- site to that side . Let ABC be a ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore