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 11
... divided by the quantity B ; the same is also represented by placing the di- vidend above the divisor , thus is equivalent to the ex- pression A ÷ B . A B 9. A power of a quantity is denoted by affixing to the quantity a small figure or ...
... divided by the quantity B ; the same is also represented by placing the di- vidend above the divisor , thus is equivalent to the ex- pression A ÷ B . A B 9. A power of a quantity is denoted by affixing to the quantity a small figure or ...
Page 13
... divided into M num- ber of units , each equal to A ' , then A = MXA ' ; and if B be divided into N number of units , each equal to A ' , then B = NXA ' ; M and N being integral numbers . The ratio of A to B will be the same as the ratio ...
... divided into M num- ber of units , each equal to A ' , then A = MXA ' ; and if B be divided into N number of units , each equal to A ' , then B = NXA ' ; M and N being integral numbers . The ratio of A to B will be the same as the ratio ...
Page 15
... divided by the other , and their product is constant . PROPOSITION I. THEOREM . If two magnitudes are expressed in terms of a unit of mag- nitude of the same kind , their sum or their difference may also be expressed in the same terms ...
... divided by the other , and their product is constant . PROPOSITION I. THEOREM . If two magnitudes are expressed in terms of a unit of mag- nitude of the same kind , their sum or their difference may also be expressed in the same terms ...
Page 17
... divided into parts , each equal to A , and R to be divided into parts each equal to B ; then by hypothe- sis , the number of the parts of P is the same as the num- ber of the parts of R. Let one of the parts of P be added to or ...
... divided into parts , each equal to A , and R to be divided into parts each equal to B ; then by hypothe- sis , the number of the parts of P is the same as the num- ber of the parts of R. Let one of the parts of P be added to or ...
Page 19
... divided is a definite magnitude , as well as the mag- nitude M , the parts of the magnitude so divided may each be expressed by numbers , or some function thereof , in terms of the unit P , which is definite also . ( Prop . V. Scholium ...
... divided is a definite magnitude , as well as the mag- nitude M , the parts of the magnitude so divided may each be expressed by numbers , or some function thereof , in terms of the unit P , which is definite also . ( Prop . V. Scholium ...
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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.