A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration, Containing Many Valuable Discoveries and Impovements in Mathematical Science ...: Designed as a Text Book for Collegiate and Academic Instruction, and as a Practical Compendium on MensurationCollins brothers & Company, 1845 |
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Página 15
... Vertical angles , such as ACO and BCN ( see dia- gram to Prop . XXI . ) are equal ; for either of them is still the angle formed by the two planes ACB , OCN . It is further evident , that , in the intersection of two arcs ACB , OCN ...
... Vertical angles , such as ACO and BCN ( see dia- gram to Prop . XXI . ) are equal ; for either of them is still the angle formed by the two planes ACB , OCN . It is further evident , that , in the intersection of two arcs ACB , OCN ...
Página 19
... vertical angle . PROPOSITION XVI . THEOREM . In any spherical triangle , the greater side is opposite the great- er angle ; and conversely , the greater angle is opposite the greater side . Let the angle A be greater than the angle B ...
... vertical angle . PROPOSITION XVI . THEOREM . In any spherical triangle , the greater side is opposite the great- er angle ; and conversely , the greater angle is opposite the greater side . Let the angle A be greater than the angle B ...
Página 26
... vertical angle of the tri - rectangular pyramid is formed by three planes , at right angles to each other . This angle , which may be called a right solid angle , will serve as a very natural unit of measure for all other solid angles ...
... vertical angle of the tri - rectangular pyramid is formed by three planes , at right angles to each other . This angle , which may be called a right solid angle , will serve as a very natural unit of measure for all other solid angles ...
Página 114
... vertical plane passing through AB ; measure the distance CD , and at C take the angles of elevation or depression of the station D , and the top and bottom of the object . Also at D take the eleva- H of the top of AB . h K Put CD = h ...
... vertical plane passing through AB ; measure the distance CD , and at C take the angles of elevation or depression of the station D , and the top and bottom of the object . Also at D take the eleva- H of the top of AB . h K Put CD = h ...
Página 127
... vertical angle ADB of a triangle to find the sides AD , DB . D On the base AB describe an isosceles triangle ACB whose vertical angle C shall be double the given angle ADB , if that angle is less than 90 ° , but double its supplement if ...
... vertical angle ADB of a triangle to find the sides AD , DB . D On the base AB describe an isosceles triangle ACB whose vertical angle C shall be double the given angle ADB , if that angle is less than 90 ° , but double its supplement if ...
Outras edições - Ver tudo
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Pré-visualização indisponível - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Pré-visualização indisponível - 2018 |
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... Nathan Scholfield Pré-visualização indisponível - 2018 |
Palavras e frases frequentes
abscissa altitude arithmetical progression axes base bisected chord circle circular circular segment circumference cone conjugate axis construction convex surface corresponding cosec cosine cylinder described diameter distance divided draw drawn ellipse equal to half equation expression feet find the solidity formed formula Geom geometrical given height hence hyperbola inches infinite series latus rectum length logarithm major axis middle frustum minor axis multiplied ordinate parabola paraboloid parallel parallelogram perpendicular plane portion prism PROBLEM Prop PROPOSITION pyramid quadrant quantity radii radius ratio rectangle revoloidal surface right angles Scholium sector segment sides similar similar triangles sine specific gravity sphere spherical triangle spheroid spindle square straight line tangent THEOREM tion transverse axis Trigonometry ungula versed sine vertex vertical virtual centre zone
Passagens conhecidas
Página 44 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Página 197 - ... is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Página 81 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 219 - 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...
Página 68 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Página 14 - ... this point of intersection, as a pole, and limited by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described about A as a pole.
Página 27 - The circumference of every circle is supposed to be divided into 360 equal parts...
Página 36 - The solidity of a cylinder is equal to the area of its base multiplied by its altitude.
Página 7 - The radius of a sphere is a straight line, drawn from the centre to any point of the surface ; the diameter, or axis, is a line passing through this centre, and terminated on both sides by the surface.