Elements of plane (solid) geometry (Higher geometry) and trigonometry (and mensuration), being the first (-fourth) part of a series on elementary and higher geometry, trigonometry, and mensuration |
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Page 7
... MEASUREMENT OF ANGLES - DEFINITIONS - GENERAL DISCUSSISON AND PROPOSITIONS - PROBLEMS RELATING TO THE SECOND AND THIRD BOOKS . BOOK FOURTH . OF THE PROPERTIES AND AREAS OF FIGURES - DEFINITIONS - GENERAL PROPOSITIONS -PROBLEMS . BOOK ...
... MEASUREMENT OF ANGLES - DEFINITIONS - GENERAL DISCUSSISON AND PROPOSITIONS - PROBLEMS RELATING TO THE SECOND AND THIRD BOOKS . BOOK FOURTH . OF THE PROPERTIES AND AREAS OF FIGURES - DEFINITIONS - GENERAL PROPOSITIONS -PROBLEMS . BOOK ...
Page 15
... measured by P , then will their sum or difference be also measured by P. Suppose the quotient of A ÷ P - Q , and B ÷ P = q . Now let A be added to B , and it is evident that their sum is as much greater than either of them , as the ...
... measured by P , then will their sum or difference be also measured by P. Suppose the quotient of A ÷ P - Q , and B ÷ P = q . Now let A be added to B , and it is evident that their sum is as much greater than either of them , as the ...
Page 16
... measured by P. P. Cor . If P measure В and also A - B or A + B , it must measure A ; for the sum of B and A - B is A , and the differ- ence of B and A + B is A. PROPOSITION II . THEOREM . If a magnitude is expressed in terms of the unit ...
... measured by P. P. Cor . If P measure В and also A - B or A + B , it must measure A ; for the sum of B and A - B is A , and the differ- ence of B and A + B is A. PROPOSITION II . THEOREM . If a magnitude is expressed in terms of the unit ...
Page 19
... measured by the unit P , can be so divided , but each part of such magnitude may also be measured by P , or some function of P : for otherwise there must be a limit to the compounding and extension of fractions , and also to ...
... measured by the unit P , can be so divided , but each part of such magnitude may also be measured by P , or some function of P : for otherwise there must be a limit to the compounding and extension of fractions , and also to ...
Page 58
Nathan Scholfield. THE CIRCLE AND THE MEASUREMENT OF ANGLES . DEFINITIONS . 1. Every line which is not a right line , or composed of right lines , is a curve line . 2. A circle is the surface terminated by a curve line , which is in ...
Nathan Scholfield. THE CIRCLE AND THE MEASUREMENT OF ANGLES . DEFINITIONS . 1. Every line which is not a right line , or composed of right lines , is a curve line . 2. A circle is the surface terminated by a curve line , which is in ...
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Elements of Plane (Solid) Geometry (Higher Geometry) and Trigonometry (and ... Nathan Scholfield No preview available - 2015 |
Common terms and phrases
ABCD abscissa altitude axis bisect chord circle circular segment circum circumference circumscribing cone conjugate construction convex surface cosec cosine cube curve cylinder described diameter distance divided draw ellipse equal to half equation equivalent feet figure formed frustum Geom geometry given hence hyperbola hypothenuse inches inscribed inscribed sphere latus rectum length logarithm magnitude measured multiplied by one-third number of sides opposite ordinates parabola parallel parallelogram perimeter perpendicular plane polyedroid polyedron polygon portion prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon revoloid rhomboid right angled triangle right line root Scholium sector segment similar similar triangles sine slant height solid angle sphere spherical square straight line tangent THEOREM triangle ABC triangular triangular prism ungula vertex vertical virtual centre
Popular passages
Page 36 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 35 - The sum of any two sides of a triangle, is greater than the third side.
Page 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 38 - The volumes of similar solids are to each other as the cubes of their like dimensions.
Page 75 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 86 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Page 211 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...
Page 48 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the exterior angles.