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 42
... vertical angle of an isosceles triangle bisects the base at right angles ; and conversely , the line bisecting the base of an isosceles trian- gle at right angles , bisects also the vertical angle . Cor . 2. Every equilateral triangle ...
... vertical angle of an isosceles triangle bisects the base at right angles ; and conversely , the line bisecting the base of an isosceles trian- gle at right angles , bisects also the vertical angle . Cor . 2. Every equilateral triangle ...
Page 72
... vertical angles are equal , and since the circumference mea- sures four right angles ( Prop . XVIII . Sch . 1. ) , it follows that the two are measured by the sum of those arcs , and also that either of them is measured by half of that ...
... vertical angles are equal , and since the circumference mea- sures four right angles ( Prop . XVIII . Sch . 1. ) , it follows that the two are measured by the sum of those arcs , and also that either of them is measured by half of that ...
Page 90
... vertical , produce the sides GE , CD , till they meet in H. The two rectangles AB- CD , AEHD , having the same altitude H D C E A B AD , are to each other as their bases G F AB , AE : in like manner the two rect- angles AEHD , AEGF ...
... vertical , produce the sides GE , CD , till they meet in H. The two rectangles AB- CD , AEHD , having the same altitude H D C E A B AD , are to each other as their bases G F AB , AE : in like manner the two rect- angles AEHD , AEGF ...
Page 132
... vertical angle . Produce AB till the rectangle AC.BC may be equivalent to the square of AB ( Prob . IV . ) , then , with the base AB and sides each equal to AC , construct the isosceles triangle DAB , and the angle A will be double the ...
... vertical angle . Produce AB till the rectangle AC.BC may be equivalent to the square of AB ( Prob . IV . ) , then , with the base AB and sides each equal to AC , construct the isosceles triangle DAB , and the angle A will be double the ...
Page 133
... vertical angle is a fifth part of two right angles , and each angle at the base is two - fifths of two right angles , or one fifth of four right angles . PROBLEM XIX . To divide a triangle ABC into two parts by a line from A , the ...
... vertical angle is a fifth part of two right angles , and each angle at the base is two - fifths of two right angles , or one fifth of four right angles . PROBLEM XIX . To divide a triangle ABC into two parts by a line from A , 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 arithmetical progression 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 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.