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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Seite 6
... Surfaces and Solids , 180 CONIC SECTIONS . The Parabola and its Properties , The Ellipse and its Properties , The Hyperbola and its Properties , 189 197 215 SPHERICAL GEOMETRY . SPHERICAL GEOMETRY . DEFINITIONS . 1. THE vi CONTENTS .
... Surfaces and Solids , 180 CONIC SECTIONS . The Parabola and its Properties , The Ellipse and its Properties , The Hyperbola and its Properties , 189 197 215 SPHERICAL GEOMETRY . SPHERICAL GEOMETRY . DEFINITIONS . 1. THE vi CONTENTS .
Seite 189
... Ellipse . 3. The Hyperbola . PARABOLA . DEFINITIONS . 1. A Parabola is a plane curve , such , that if from any point in the curve two straight lines be drawn ; one to a given fixed point , the other perpendicular to a straight line ...
... Ellipse . 3. The Hyperbola . PARABOLA . DEFINITIONS . 1. A Parabola is a plane curve , such , that if from any point in the curve two straight lines be drawn ; one to a given fixed point , the other perpendicular to a straight line ...
Seite 196
... any diameter is equal to the rectangle under the parameter and abscissa It will be seen , that Prop . VII . is a particular case of the present proposition . ELLIPSE . DEFINITIONS . 1. AN ELLIPSE is a plane 196 CONIC SECTIONS .
... any diameter is equal to the rectangle under the parameter and abscissa It will be seen , that Prop . VII . is a particular case of the present proposition . ELLIPSE . DEFINITIONS . 1. AN ELLIPSE is a plane 196 CONIC SECTIONS .
Seite 197
Nathan Scholfield. ELLIPSE . DEFINITIONS . 1. AN ELLIPSE is a plane curve , such that , if from any point in the curve two straight lines be drawn to two given fixed points , the sum of these straight lines will always be the same . 2 ...
Nathan Scholfield. ELLIPSE . DEFINITIONS . 1. AN ELLIPSE is a plane curve , such that , if from any point in the curve two straight lines be drawn to two given fixed points , the sum of these straight lines will always be the same . 2 ...
Seite 199
... . point in the curve . For , SP + HP = Aa . SP + HP AS + AH = AS + AH = AS + SH , And , SP + HP = aS + aH = 2 aH + SH , Def . 1 . .. 2 ( SP + HP ) = 2 ( ÁS + SH + Ha ) That is , if P be any Or , SP + HP Aa . Cor . The ELLIPSE . 199.
... . point in the curve . For , SP + HP = Aa . SP + HP AS + AH = AS + AH = AS + SH , And , SP + HP = aS + aH = 2 aH + SH , Def . 1 . .. 2 ( SP + HP ) = 2 ( ÁS + SH + Ha ) That is , if P be any Or , SP + HP Aa . Cor . The ELLIPSE . 199.
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Elements of Plane (Solid) Geometry (Higher Geometry) and Trigonometry (and ... Nathan Scholfield Keine Leseprobe verfügbar - 2015 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 36 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Seite 116 - E to A, from A to B, from B to C, and from C to...
Seite 35 - The sum of any two sides of a triangle, is greater than the third side.
Seite 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Seite 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Seite 38 - The volumes of similar solids are to each other as the cubes of their like dimensions.
Seite 75 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Seite 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...
Seite 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...
Seite 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.