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 |
From inside the book
Results 1-5 of 50
Page 51
... one right angle . Cor . 5. Since every equilateral triangle is also equiangu- lar ( Prop . XIV . Cor . 2. ) , each of its angles will be equal to the third ... multiplied by 4-2 , which amounts to four right angles ; hence , if all the ...
... one right angle . Cor . 5. Since every equilateral triangle is also equiangu- lar ( Prop . XIV . Cor . 2. ) , each of its angles will be equal to the third ... multiplied by 4-2 , which amounts to four right angles ; hence , if all the ...
Page 120
... one at D , the other at A also the angle B - E ; these triangles are therefore similar , and they give the proportion AB : CE :: AD : AC ; hence AB.AC-CE.AD . D Cor . If these equal quantities be multiplied by the 120 ELEMENTS OF GEOMETRY .
... one at D , the other at A also the angle B - E ; these triangles are therefore similar , and they give the proportion AB : CE :: AD : AC ; hence AB.AC-CE.AD . D Cor . If these equal quantities be multiplied by the 120 ELEMENTS OF GEOMETRY .
Page 168
... one generally used . Scholium . We shall have occasion to recur to this subject again , in a subsequent volume ... multiplied by its dis- tance from the second + the area of the inner circle ; and the annular space between the second and ...
... one generally used . Scholium . We shall have occasion to recur to this subject again , in a subsequent volume ... multiplied by its dis- tance from the second + the area of the inner circle ; and the annular space between the second and ...
Page 40
... three dimensions . For , having placed the two solids AG , AZ , ( see diagram to Prop . XIV . ) , so that their surfaces have the common angle BAE , produce the planes necessary for completing the third ... one dimension of the base ...
... three dimensions . For , having placed the two solids AG , AZ , ( see diagram to Prop . XIV . ) , so that their surfaces have the common angle BAE , produce the planes necessary for completing the third ... one dimension of the base ...
Page 53
... multiplied by one third of SO ; hence every pyramid is measured by a third part of the product of its base by its altitude . Cor . 1. Every pyramid is the third part of a prism which has the same base and the same altitude . Cor . 2 ...
... multiplied by one third of SO ; hence every pyramid is measured by a third part of the product of its base by its altitude . Cor . 1. Every pyramid is the third part of a prism which has the same base and the same altitude . Cor . 2 ...
Other editions - View all
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.