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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Resultat 1-5 av 100
Side 25
... follows ( Prop . XIII . ) mM : N :: mP : Q , and nO : N :: nR : Q. Let N ' be a submultiple of N less than mM - nO , and take Q ' an equi - submultiple of Q ; then N ' must be contained oft- ener in mM than in nO . Now ( Prop . XIII ...
... follows ( Prop . XIII . ) mM : N :: mP : Q , and nO : N :: nR : Q. Let N ' be a submultiple of N less than mM - nO , and take Q ' an equi - submultiple of Q ; then N ' must be contained oft- ener in mM than in nO . Now ( Prop . XIII ...
Side 26
... follows from the last corollary by inverting the terms of the proportions . PROPOSITION XXI . THEOREM . If the antecedents in one proportion be the same as those in another , then the first antecedent is to the sum or difference of the ...
... follows from the last corollary by inverting the terms of the proportions . PROPOSITION XXI . THEOREM . If the antecedents in one proportion be the same as those in another , then the first antecedent is to the sum or difference of the ...
Side 39
... follows the converse of the corollary to Prop . VIII . , viz : if a perpendi- cular from one of the angles of a triangle to the opposite side bisect this angle , it shall also bisect the side on which it falls , so that the sides ...
... follows the converse of the corollary to Prop . VIII . , viz : if a perpendi- cular from one of the angles of a triangle to the opposite side bisect this angle , it shall also bisect the side on which it falls , so that the sides ...
Side 41
... follow by the last proposi- tion , that the side EF must be greater than BC ; and if the angle D were less than A , it would follow , that ... follows ( Prop . VIII . Cor . 2. ) that BD is equal to CD , and that the angle ADB 6 BOOK II . 41.
... follow by the last proposi- tion , that the side EF must be greater than BC ; and if the angle D were less than A , it would follow , that ... follows ( Prop . VIII . Cor . 2. ) that BD is equal to CD , and that the angle ADB 6 BOOK II . 41.
Side 42
... follows that the same triangles are equal ( Prop . VIII . ) , which is im- possible ; therefore AB cannot be longer than AC , and in a similar manner it may be shown that AC cannot be longer than AB ; therefore these two sides are equal ...
... follows that the same triangles are equal ( Prop . VIII . ) , which is im- possible ; therefore AB cannot be longer than AC , and in a similar manner it may be shown that AC cannot be longer than AB ; therefore these two sides are equal ...
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Elements of Plane (Solid) Geometry (Higher Geometry) and Trigonometry (and ... Nathan Scholfield Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 36 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Side 35 - The sum of any two sides of a triangle, is greater than the third side.
Side 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Side 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Side 38 - The volumes of similar solids are to each other as the cubes of their like dimensions.
Side 75 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Side 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...
Side 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...
Side 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.