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
... square root of 2 ; AXB or ✓ ( AXB ) means the square root of the product of A and B. 11. The symbol .. is used to denote the word hence or therefore ; indicating a conclusion , depending on the fore- going premises . AXIOMS . 1 ...
... square root of 2 ; AXB or ✓ ( AXB ) means the square root of the product of A and B. 11. The symbol .. is used to denote the word hence or therefore ; indicating a conclusion , depending on the fore- going premises . AXIOMS . 1 ...
Page 91
... square . If the side of the square is a linear inch , the rectangle contains 18 square inches ; if the side of the square is a foot , the rectan- gle contains 18 square feet . PROPOSITION VII . THEOREM . The area of any rhomboid is ...
... square . If the side of the square is a linear inch , the rectangle contains 18 square inches ; if the side of the square is a foot , the rectan- gle contains 18 square feet . PROPOSITION VII . THEOREM . The area of any rhomboid is ...
Page 93
... square ACDE is made up of four parts ; the first ABIF is the square described on AB , since we made AF - AB : the second IGDHA H B D G is the square described on IG , or BC ; for since we have AC = AE and AB = AF , the difference AC ...
... square ACDE is made up of four parts ; the first ABIF is the square described on AB , since we made AF - AB : the second IGDHA H B D G is the square described on IG , or BC ; for since we have AC = AE and AB = AF , the difference AC ...
Page 94
... square of the part AD , and be the square of the part DC , and Nʊ E the square of the part BC , and the com- plements of these several squares are Df Fe , each equal to ADXDC , and O CE , each equal to ADXCB , and Ib - Eb , each equal ...
... square of the part AD , and be the square of the part DC , and Nʊ E the square of the part BC , and the com- plements of these several squares are Df Fe , each equal to ADXDC , and O CE , each equal to ADXCB , and Ib - Eb , each equal ...
Page 95
... square ABIF minus the square DHIG , which latter is equal to a square described on BC : hence we have ( AB + AC ) × ( AB — BC ) = AB2 — BC2 . Scholium . This proposition is equivalent to the algebraical formula , ( a + b ) × ( a — b ) ...
... square ABIF minus the square DHIG , which latter is equal to a square described on BC : hence we have ( AB + AC ) × ( AB — BC ) = AB2 — BC2 . Scholium . This proposition is equivalent to the algebraical formula , ( a + b ) × ( a — b ) ...
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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.