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 61
... radius , perpendicular to a chord , bisects the chord , and bi- sects also the subtended arc of the chord . Let AB be a chord , and CG the radius perpendicular to it : then will AD - DB , and the arc AG = GB . For , draw the radii CA ...
... radius , perpendicular to a chord , bisects the chord , and bi- sects also the subtended arc of the chord . Let AB be a chord , and CG the radius perpendicular to it : then will AD - DB , and the arc AG = GB . For , draw the radii CA ...
Seite 64
... radius CB , it shall touch the circle in the point A B. B ED For to show that this point B is the only one which the ... radius CB ; hence in reference to this new tangent , the radius CB would be an oblique line , and the perpendicular ...
... radius CB , it shall touch the circle in the point A B. B ED For to show that this point B is the only one which the ... radius CB ; hence in reference to this new tangent , the radius CB would be an oblique line , and the perpendicular ...
Seite 65
... radius CH perpendicular to the chord MP . It will , at the same time be perpendicular to NI . ( Prop . XXIII . Cor . 1. B. II ) ; therefore , the point H will be at once the middle of the arc MHP , and of the arc NHL ( Prop . VI ...
... radius CH perpendicular to the chord MP . It will , at the same time be perpendicular to NI . ( Prop . XXIII . Cor . 1. B. II ) ; therefore , the point H will be at once the middle of the arc MHP , and of the arc NHL ( Prop . VI ...
Seite 66
... radius CH ; hence , as both chords are bisected by this radius , they are perpendicular to it ( Prop . VI . ) ; that is , they are parallel . PROPOSITION XII . THEOREM . If two circles cut each other in two points , the line which joins ...
... radius CH ; hence , as both chords are bisected by this radius , they are perpendicular to it ( Prop . VI . ) ; that is , they are parallel . PROPOSITION XII . THEOREM . If two circles cut each other in two points , the line which joins ...
Seite 74
... radius CA , and from the point D draw the secant DA to the extremity of the radius , cutting off AF an arc of the circle ; then will the angle formed by the meet- ing of the lines at D be equal to an angle measured by half the arc AF ...
... radius CA , and from the point D draw the secant DA to the extremity of the radius , cutting off AF an arc of the circle ; then will the angle formed by the meet- ing of the lines at D be equal to an angle measured by half the arc AF ...
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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
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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.