Elements of Geometry: With Practical Applications to Mensuration |
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Page 13
... drawn from one point to another . 11. From one point to another only one straight line can be drawn . 12. Through the same point only one parallel to a straight line can be drawn . 13. All right angles are equal to one another . 2 BOOK I.
... drawn from one point to another . 11. From one point to another only one straight line can be drawn . 12. Through the same point only one parallel to a straight line can be drawn . 13. All right angles are equal to one another . 2 BOOK I.
Page 14
... drawn through a given point parallel to another straight line . 4. That a perpendicular to a given straight line may be drawn from a point either within or without the line . 5. That an angle may be described equal to any given angle ...
... drawn through a given point parallel to another straight line . 4. That a perpendicular to a given straight line may be drawn from a point either within or without the line . 5. That an angle may be described equal to any given angle ...
Page 15
... drawn perpendicular to A B ; then the angles ACE and E C B will each be a right angle ( Art . 15 ) . But the angle A CD is composed of the right angle A CE and the angle ECD ( Art . 34 , Ax . 9 ) , and the angles ECD and DCB compose the ...
... drawn perpendicular to A B ; then the angles ACE and E C B will each be a right angle ( Art . 15 ) . But the angle A CD is composed of the right angle A CE and the angle ECD ( Art . 34 , Ax . 9 ) , and the angles ECD and DCB compose the ...
Page 17
... drawn , making , with CA , the right angle ACF . Now , since ACD is a straight line , the angle FCD will be a right angle ( Prop . I. Cor . 1 ) ; and since ACE is a straight line , the angle FCE will also be a right angle ; therefore ...
... drawn , making , with CA , the right angle ACF . Now , since ACD is a straight line , the angle FCD will be a right angle ( Prop . I. Cor . 1 ) ; and since ACE is a straight line , the angle FCE will also be a right angle ; therefore ...
Page 21
... drawn from the point A to the point B ( Art . 34 , Ax . 10 ) ; hence the side A B is less than the sum of the sides ... Draw the straight line CD , making the angle B C D equal to B. Then , in c the triangle BDC , we shall have the A D B ...
... drawn from the point A to the point B ( Art . 34 , Ax . 10 ) ; hence the side A B is less than the sum of the sides ... Draw the straight line CD , making the angle B C D equal to B. Then , in c the triangle BDC , we shall have the A D B ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle ACB angle equal arc A B base bisect chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Popular passages
Page 59 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 37 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 120 - At a point in a given straight line to make an angle equal to a given angle.
Page 52 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Page 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.