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 33
... ABCD , is a diagonal . B. 34. Plane figures are equal , when , by supposing them to be applied to each other , they would coincide throughout ; and they are said to be equivalent , when they enclose equal portions of space , and are at ...
... ABCD , is a diagonal . B. 34. Plane figures are equal , when , by supposing them to be applied to each other , they would coincide throughout ; and they are said to be equivalent , when they enclose equal portions of space , and are at ...
Page 52
... ABCD- FG , be produced , in the same direc- tion ; then will the sum of the exteri- or angles a + b + c + d + f + g , be equal to four right angles . For , each interior angle , plus its ex- terior angle , as A + a , is equal to two ...
... ABCD- FG , be produced , in the same direc- tion ; then will the sum of the exteri- or angles a + b + c + d + f + g , be equal to four right angles . For , each interior angle , plus its ex- terior angle , as A + a , is equal to two ...
Page 54
... ABCD be a rhomboid , the opposite sides and angles are equal . ୯ B D Draw the diagonal AC ; then , since AB , DC , are parallel , the alternate an- gles BAC , DCA , are equal ( Pr . XXIII . Cor . 3. ) , and because AD , BC , are also ...
... ABCD be a rhomboid , the opposite sides and angles are equal . ୯ B D Draw the diagonal AC ; then , since AB , DC , are parallel , the alternate an- gles BAC , DCA , are equal ( Pr . XXIII . Cor . 3. ) , and because AD , BC , are also ...
Page 55
... ABCD ( preceding diagram ) , let AB be equal and parallel to DC , then will ABCD be a rhomboid . For the diagonal AC makes the alternate angles BAC , DCA , equal ( Prop . XXIII . Cor . 2. ) ; so that in the triangles ABC , CDA , two ...
... ABCD ( preceding diagram ) , let AB be equal and parallel to DC , then will ABCD be a rhomboid . For the diagonal AC makes the alternate angles BAC , DCA , equal ( Prop . XXIII . Cor . 2. ) ; so that in the triangles ABC , CDA , two ...
Page 56
... ABCD is a rhomboid . Cor . If , in addition , the parallel sides be each equal to a third side , the rhomboid will be either a rhombus or a square , according as it has , or has not , a right angle . Scholium . It has been proved ( Prop ...
... ABCD is a rhomboid . Cor . If , in addition , the parallel sides be each equal to a third side , the rhomboid will be either a rhombus or a square , according as it has , or has not , a right angle . Scholium . It has been proved ( Prop ...
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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.