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 9
... length , breadth and thickness . Lines are obviously the boundaries of surfaces , and surfa- ces are the boundaries of solids ; it is equally obvious that a line being mere length , without either breadth or thickness , can exist only ...
... length , breadth and thickness . Lines are obviously the boundaries of surfaces , and surfa- ces are the boundaries of solids ; it is equally obvious that a line being mere length , without either breadth or thickness , can exist only ...
Page 29
... length , breadth , and height or thick- ness ; and hence results magnitude . 2. Magnitude , being the result of extension , must neces- sarily occupy space ; therefore all magnitudes possess local- ity . 3. Locality , or position , is a ...
... length , breadth , and height or thick- ness ; and hence results magnitude . 2. Magnitude , being the result of extension , must neces- sarily occupy space ; therefore all magnitudes possess local- ity . 3. Locality , or position , is a ...
Page 31
... length and breadth without thickness . 19. A plane is a surface in which if two points be as- sumed at pleasure and connected by a right line , that line will lie wholly in the surface . 20. Every surface which is not a plane surface ...
... length and breadth without thickness . 19. A plane is a surface in which if two points be as- sumed at pleasure and connected by a right line , that line will lie wholly in the surface . 20. Every surface which is not a plane surface ...
Page 91
... length , or a lin- ear unit . For example , if the length of the rectangle A is six units and its alti- tude three , then 6x3 , or 18 , represents the number of superficial units or squares contained in the rectangle , and each side ...
... length , or a lin- ear unit . For example , if the length of the rectangle A is six units and its alti- tude three , then 6x3 , or 18 , represents the number of superficial units or squares contained in the rectangle , and each side ...
Page 116
... length of the perpendicular BD , but the area may be determined by having the two sides and their included angle given , half the product of which must be multiplied by the sine of such an- gle ; and the sine may be shown to be the ...
... length of the perpendicular BD , but the area may be determined by having the two sides and their included angle given , half the product of which must be multiplied by the sine of such an- gle ; and the sine may be shown to be the ...
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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.