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 58
... circle to the circumference , and it follows from Def . 2. that all radii are equal . 5. The diameter of a circle is a right line drawn through the centre . Hence , according to Def . 4 , it is twice the ra- dius . H In the annexed ...
... circle to the circumference , and it follows from Def . 2. that all radii are equal . 5. The diameter of a circle is a right line drawn through the centre . Hence , according to Def . 4 , it is twice the ra- dius . H In the annexed ...
Page 59
... circle is said to circumscribe a polygon . 17. A circle is inscribed in a polygon , when all its sides touch the circumference , and the polygon is said to circum- scribe the circle . 18. By an angle in the segment of a circle , is ...
... circle is said to circumscribe a polygon . 17. A circle is inscribed in a polygon , when all its sides touch the circumference , and the polygon is said to circum- scribe the circle . 18. By an angle in the segment of a circle , is ...
Page 60
... circle or in equal circles , equal arcs are subtended by equal chords ; and conversely , equal chords subtend equal arcs . H If the radii AC , EO , are D equal , and the arcs AMD , M // ENG ; then the chord AD will be equal to the chord ...
... circle or in equal circles , equal arcs are subtended by equal chords ; and conversely , equal chords subtend equal arcs . H If the radii AC , EO , are D equal , and the arcs AMD , M // ENG ; then the chord AD will be equal to the chord ...
Page 64
... circle in the point A B. C B ED For to show that this point B is the only one which the circle has in common with AD , let CE be drawn to any other point E in that line , then CE being longer than CB , ( Prop . XVII . B. II . ) the ...
... circle in the point A B. C B ED For to show that this point B is the only one which the circle has in common with AD , let CE be drawn to any other point E in that line , then CE being longer than CB , ( Prop . XVII . B. II . ) the ...
Page 67
... circles is equal to the difference of their radii , the two circles will touch each other internally . Let C and D be the centres at a dis - E tance from each other equal to AD- CA. It is evident , as before , that they will have the ...
... circles is equal to the difference of their radii , the two circles will touch each other internally . Let C and D be the centres at a dis - E tance from each other equal to AD- CA. It is evident , as before , that they will have the ...
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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 arithmetical progression 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 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.