Elements of Geometry and Trigonometry |
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Page 45
... determine the position of a straight line ; hence every straight line which passes through two of the points just mentioned , will necessarily pass through the third , and be perpendicular to the chord . It follows , likewise , that the ...
... determine the position of a straight line ; hence every straight line which passes through two of the points just mentioned , will necessarily pass through the third , and be perpendicular to the chord . It follows , likewise , that the ...
Page 58
... determine a line , AD is that perpendicular . Scholium . The same construction serves for making a right angle BAD , at a given point A , on a given straight line BC . PROBLEM III . From a given point , without a straight line , to let ...
... determine a line , AD is that perpendicular . Scholium . The same construction serves for making a right angle BAD , at a given point A , on a given straight line BC . PROBLEM III . From a given point , without a straight line , to let ...
Page 85
... determines the similarity of two triangles . The case is different with regard to figures of more than three sides : even in quadrilaterals , the proportion between the sides may be altered without altering the angles , or the angles ...
... determines the similarity of two triangles . The case is different with regard to figures of more than three sides : even in quadrilaterals , the proportion between the sides may be altered without altering the angles , or the angles ...
Page 108
... determine whether the lines AC , CB , have or have not a common measure . There is a very simple way , however , of avoiding these decreasing lines , A F and obtaining the result , by operating B E only upon lines which remain always of ...
... determine whether the lines AC , CB , have or have not a common measure . There is a very simple way , however , of avoiding these decreasing lines , A F and obtaining the result , by operating B E only upon lines which remain always of ...
Page 109
... , like the angle of an equiangular polygon , is determined by the number of its sides ( Book I. Prop . XXVI . ) . PROPOSITION II . THEOREM . Any regular polygon may be BOOK V. 109 BOOK V Regular Polygons and the Measurement of the Circle,
... , like the angle of an equiangular polygon , is determined by the number of its sides ( Book I. Prop . XXVI . ) . PROPOSITION II . THEOREM . Any regular polygon may be BOOK V. 109 BOOK V Regular Polygons and the Measurement of the Circle,
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex