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
... 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 common , and the angle CBA ABE ; hence the sides AC ...
... 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 common , and the angle CBA ABE ; hence the sides AC ...
Page 49
... Hence , from the same point more than one parallel to a right line cannot be drawn . PROPOSITION XXV . THEOREM . Two ... Hence AB R P B and CD are perpendicular to the same straight line ; hence they are parallel ( Prop XXI ...
... Hence , from the same point more than one parallel to a right line cannot be drawn . PROPOSITION XXV . THEOREM . Two ... Hence AB R P B and CD are perpendicular to the same straight line ; hence they are parallel ( Prop XXI ...
Page 50
... hence , the angle DEF is equal to BAC ( Ax . 1. ) Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC , and ED in the same direction with AB , is necessary , because if FE were ...
... hence , the angle DEF is equal to BAC ( Ax . 1. ) Scholium . The restriction of this proposition to the case where the side EF lies in the same direction with AC , and ED in the same direction with AB , is necessary , because if FE were ...
Page 61
... hence , the third side AH is greater than the third side AD ( Prop . XII . B. II . ) : therefore the chord , which subtends the greater arc , is the greater . K Conversely , if the chord AH is greater than AD , it will follow , on ...
... hence , the third side AH is greater than the third side AD ( Prop . XII . B. II . ) : therefore the chord , which subtends the greater arc , is the greater . K Conversely , if the chord AH is greater than AD , it will follow , on ...
Page 62
... hence there would be two perpendiculars , BF , BK , let fall from the same point B , on the same straight line , which is impossible ( Prop . I. B. II . ) ; hence , DE , FG , will al- ways meet in some point 0 . And moreover , this ...
... hence there would be two perpendiculars , BF , BK , let fall from the same point B , on the same straight line , which is impossible ( Prop . I. B. II . ) ; hence , DE , FG , will al- ways meet in some point 0 . And moreover , this ...
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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.