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 4
... shown that our reasoning in reference to such quantities ought not to be embarrassed on account of their incommensurability , since any magnitude may , as will be shown , be expressed by some function of any other magnitude , aud hence ...
... shown that our reasoning in reference to such quantities ought not to be embarrassed on account of their incommensurability , since any magnitude may , as will be shown , be expressed by some function of any other magnitude , aud hence ...
Page 17
... shown that if two magnitudes arc like submultiples of two others , the sum or difference of the former submultiples will be the same submultiple of the sum or difference of the latter . Scholium . Having proved it of two magnitudes , it ...
... shown that if two magnitudes arc like submultiples of two others , the sum or difference of the former submultiples will be the same submultiple of the sum or difference of the latter . Scholium . Having proved it of two magnitudes , it ...
Page 18
... shown that the required mea- sure must also measure E , and so on as long as there are any remainders . Now let us ... shown to measure , E must measure B ; it must therefore measure a multiple of B ; and since the difference between A ...
... shown that the required mea- sure must also measure E , and so on as long as there are any remainders . Now let us ... shown to measure , E must measure B ; it must therefore measure a multiple of B ; and since the difference between A ...
Page 20
... shown the relation of numbers to magnitude . And moreover , we shall use the former letters , A , B , C , & c . , of the alphabet to denote mag- nitudes , and the latter letters , Q , R , S , & c . , to denote the nu- merical ...
... shown the relation of numbers to magnitude . And moreover , we shall use the former letters , A , B , C , & c . , of the alphabet to denote mag- nitudes , and the latter letters , Q , R , S , & c . , to denote the nu- merical ...
Page 25
... shown above M : 0 :: P R , and since O : T :: R : S , it follows by the preceding case that MT :: P : S , and so on for any number of magni- tudes . Cor . 1. If the consequents of one proportion be the ante- cedents in another , a third ...
... shown above M : 0 :: P R , and since O : T :: R : S , it follows by the preceding case that MT :: P : S , and so on for any number of magni- tudes . Cor . 1. If the consequents of one proportion be the ante- cedents in another , a third ...
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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.