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 89
... bases and alti- tudes equal ; for it has been shown ( Prop . I. ) that the rhom- boids AG , GC , are equivalent ( see the diagram ) where the base GF must be longer than the base GE , provided AB is longer than AD , for then the angle ...
... bases and alti- tudes equal ; for it has been shown ( Prop . I. ) that the rhom- boids AG , GC , are equivalent ( see the diagram ) where the base GF must be longer than the base GE , provided AB is longer than AD , for then the angle ...
Page 91
... base by its altitude . For , the parallelogram ABCD is equiva- lent to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . III . Cor . ) : but this rectangle is measured by ABX BE ( Prop . VI . Sch ...
... base by its altitude . For , the parallelogram ABCD is equiva- lent to the rectangle ABEF , which has the same base AB , and the same altitude BE ( Prop . III . Cor . ) : but this rectangle is measured by ABX BE ( Prop . VI . Sch ...
Page 110
... base by the rectangle EL ; and in the second case that they exceed it by the rectangle EL . Lastly , that if the triangle be right angled at B , as the rectangle EL vanishes , the sum of the squares of the sides is equal to the square ...
... base by the rectangle EL ; and in the second case that they exceed it by the rectangle EL . Lastly , that if the triangle be right angled at B , as the rectangle EL vanishes , the sum of the squares of the sides is equal to the square ...
Page 114
... base drawn from one of its angles to meet the opposite side produced , is equal to half the product of the base with the difference of per- pendiculars from the other two angles to this base . Let ABC be a triangle , and let BD be a base ...
... base drawn from one of its angles to meet the opposite side produced , is equal to half the product of the base with the difference of per- pendiculars from the other two angles to this base . Let ABC be a triangle , and let BD be a base ...
Page 115
... base , instead of being exterior , should Α fall within the triangle , as BD , then the area of the triangle ABC is equal to half the product of the base BD into the sum of the perpendicu- lars AF + CH let fall from the angles A ani C ...
... base , instead of being exterior , should Α fall within the triangle , as BD , then the area of the triangle ABC is equal to half the product of the base BD into the sum of the perpendicu- lars AF + CH let fall from the angles A ani C ...
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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.