Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids: to which are Added, Edlemnts of Plane and Spherical TrigonometryW.E. Dean, 1836 - 311 páginas |
Dentro del libro
Resultados 1-5 de 38
Página 310
... Sine of the arch AC , or of the angle ABC , of which AC is the measure . COR . 1. The sine of a quadrant , or of a right angle , is equal to the radius . F L D srij To colher COR . 2. The sine of an arch is half the chord of twice that ...
... Sine of the arch AC , or of the angle ABC , of which AC is the measure . COR . 1. The sine of a quadrant , or of a right angle , is equal to the radius . F L D srij To colher COR . 2. The sine of an arch is half the chord of twice that ...
Página 311
... sine , tangent , and secant of any angle ABC , are likewise the sine , tangent , and secant of its supplement CBF , It is manifest from Def . 4. that CD is the sine of the angle CBF . Let CB be produced till it meet the circle again in ...
... sine , tangent , and secant of any angle ABC , are likewise the sine , tangent , and secant of its supplement CBF , It is manifest from Def . 4. that CD is the sine of the angle CBF . Let CB be produced till it meet the circle again in ...
Página 312
... sine , tangent , or secant of the complement of any angle is called the Cosine , Cotangent , or Cosecant of that angle . Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant of ...
... sine , tangent , or secant of the complement of any angle is called the Cosine , Cotangent , or Cosecant of that angle . Thus , let CL or DB , which is equal to CL , be the sine of the angle CBH ; HK the tangent , and BK the secant of ...
Página 313
... sine of the angle opposite to that side : and as either of the sides is to the other side , so is the radius to the tangent of the angle opposite to that side , Let ABC be a right angled plane triangle , of which BC is the hypotenuse ...
... sine of the angle opposite to that side : and as either of the sides is to the other side , so is the radius to the tangent of the angle opposite to that side , Let ABC be a right angled plane triangle , of which BC is the hypotenuse ...
Página 316
... sine of the arch AC ; and BH or LK be- ing the sine of AB , DK is the sum of the sines of the arches AC and AB , and CK is the difference of their sines ; DAB also G is the sum of the arches AC and AB , because AD equal to AC , and BC ...
... sine of the arch AC ; and BH or LK be- ing the sine of AB , DK is the sum of the sines of the arches AC and AB , and CK is the difference of their sines ; DAB also G is the sum of the arches AC and AB , because AD equal to AC , and BC ...
Otras ediciones - Ver todas
Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism proportional proposition pyramid Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle spherical angle spherical triangle Spherical Trigonometry straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 58 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 26 - If two triangles have two sides of the one equal to two sides of the...
Página 46 - Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. s«e N. Ij'a straight line fall upon two parallel straight lines, it makes the alternate angles equal...
Página 74 - THEOR. //' a straight line be divided into two equal, and also into two unequal parts, the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
Página 84 - An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight . line which is the base of the segment.
Página 411 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 112 - 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.
Página 118 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 54 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Página 49 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.