Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous Practical ProblemsIvison, Blakeman, Taylor, 1860 - 453 sider |
Inni boken
Resultat 1-5 av 42
Side 45
... represent any triangle , AB D its base , and AD , at right angles to AB , its altitude ; now we are to show that the area of ABC is equal to the product of AB by one half of AD ; or one half of AB by AD ; or one half of the product of ...
... represent any triangle , AB D its base , and AD , at right angles to AB , its altitude ; now we are to show that the area of ABC is equal to the product of AB by one half of AD ; or one half of AB by AD ; or one half of the product of ...
Side 47
... represent any whole right line divided into any two parts a and b ; then we shall have the equation w = a + b By squaring , w2 = a2 + b2 + 2ab . = Cor . If ab , then w2 b , then w2 4a2 ; that is , the square de- scribed on any line is ...
... represent any whole right line divided into any two parts a and b ; then we shall have the equation w = a + b By squaring , w2 = a2 + b2 + 2ab . = Cor . If ab , then w2 b , then w2 4a2 ; that is , the square de- scribed on any line is ...
Side 48
... represent the greater of two lines , b the less , and their difference ; then we must have this equation : d = α - b By squaring , d2 = a2 + b2 - 2ab . a a2 Cor . If db , then d = and d2 = 2 4 that is , the square described on one half ...
... represent the greater of two lines , b the less , and their difference ; then we must have this equation : d = α - b By squaring , d2 = a2 + b2 - 2ab . a a2 Cor . If db , then d = and d2 = 2 4 that is , the square described on one half ...
Side 49
... represent one line , and b another ; Then a + b is their sum , and a - b their difference ; and ( a + b ) × ( a — b ) — a2 — b2 . = THEOREM XXXIX . The square described on the hypotenuse of any right - angled triangle is equivalent to ...
... represent one line , and b another ; Then a + b is their sum , and a - b their difference ; and ( a + b ) × ( a — b ) — a2 — b2 . = THEOREM XXXIX . The square described on the hypotenuse of any right - angled triangle is equivalent to ...
Side 54
... represent any triangle ; Can acute angle , CB the base , and AD the perpendicular , C which falls either A A α B x without or on the base . Now we are to a prove that AB2 = CB2 + AC2 — 2CB × CD . From the first figure we get BD = CD ...
... represent any triangle ; Can acute angle , CB the base , and AD the perpendicular , C which falls either A A α B x without or on the base . Now we are to a prove that AB2 = CB2 + AC2 — 2CB × CD . From the first figure we get BD = CD ...
Andre utgaver - Vis alle
Elements of Geometry and Plane and Spherical Trigonometry: With Numerous ... Horatio Nelson Robinson Uten tilgangsbegrensning - 1867 |
Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ... Horatio Nelson Robinson Uten tilgangsbegrensning - 1865 |
Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ... Horatio Nelson Robinson Uten tilgangsbegrensning - 1860 |
Vanlige uttrykk og setninger
ABCD altitude angle opposite axis bisected chord circle circumference circumscribed common cone convex surface cos.a cos.b cos.c Cosine Cotang diagonal diameter dicular difference distance divided draw equal angles equation equiangular equivalent find the angles formulæ four magnitudes frustum given line greater half Hence the theorem homologous hypotenuse included angle inscribed intersect isosceles less Let ABC logarithm measured multiplied N.sine number of sides opposite angles parallelogram parallelopipedon pendicular perpen perpendicular plane ST polyedron PROBLEM produced Prop proportion PROPOSITION prove pyramid quadrantal radii radius rectangle regular polygon right angles right-angled spherical triangle right-angled triangle SCHOLIUM secant segment similar sin.a sin.b sin.c sine solid angles sphere SPHERICAL TRIGONOMETRY straight line subtracting Tang tangent three angles three sides triangle ABC triangular prisms TRIGONOMETRY vertex vertical angle volume
Populære avsnitt
Side 320 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 65 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Side 121 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF.
Side 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Side 34 - Conversely: if two angles of a triangle are equal, the sides opposite to them are equal, and the triangle it itosceles.
Side 126 - To inscribe a regular polygon of a certain number of sides in a given circle, we have only to divide the circumference into as many equal parts as the polygon has sides : for the arcs being equal, the chords AB, BC, CD, &c.
Side 22 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Side 277 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Side 94 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Side 30 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.