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 43
... half of ABF , is shorter than AC , the half of ACF ; hence , the perpendicular is shorter than any oblique line . Secondly . Let us suppose BC - BE ; then will the triangle CAB be equal to the triangle BAE ; for BC - BE , the side AB is ...
... half of ABF , is shorter than AC , the half of ACF ; hence , the perpendicular is shorter than any oblique line . Secondly . Let us suppose BC - BE ; then will the triangle CAB be equal to the triangle BAE ; for BC - BE , the side AB is ...
Page 63
... half of AB , is equal to the side DG , the half of DE ; hence the triangles are equal , and CF is equal to CG , ( Prop . XIX . B. II . ) ; hence , the two equal chords AB , DE , are equally distant from the centre . K Secondly . Let the ...
... half of AB , is equal to the side DG , the half of DE ; hence the triangles are equal , and CF is equal to CG , ( Prop . XIX . B. II . ) ; hence , the two equal chords AB , DE , are equally distant from the centre . K Secondly . Let the ...
Page 71
... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence , BAC + CAD , or BAD , will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle ...
... half of BE . For a like reason , the angle CAD will be measured by the half of ED ; hence , BAC + CAD , or BAD , will be measured by half of BE + ED , or of BED . Suppose , in the second place , that the centre C lies without the angle ...
Page 72
... half of the arc BOC , less than a semi - circumference . And every angle BOC , inscribed in a seg- ment less than a semicircle , is an obtuse an- B gle ; for it is measured by half of the arc BAC , greater than a semi - circumference ...
... half of the arc BOC , less than a semi - circumference . And every angle BOC , inscribed in a seg- ment less than a semicircle , is an obtuse an- B gle ; for it is measured by half of the arc BAC , greater than a semi - circumference ...
Page 73
... half the semi - circumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC , is mea- sured by the half of AMD plus the half of DC , or by half the whole arc AMDC . M B D E It might be shown , by taking ...
... half the semi - circumference AMD ; the angle DAC is measured by the half of DC : hence , BAD + DAC , or BAC , is mea- sured by the half of AMD plus the half of DC , or by half the whole arc AMDC . M B D E It might be shown , by taking ...
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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.