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 |
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Página 26
... angle BAC be also equal to the angle EDF : then shall the base BC be equal to the base E ; and the tri- angle ABC to the triangle DEF ; B CE D and the other angles , to which the equal sides are oppo- site , shall be equal , each to ...
... angle BAC be also equal to the angle EDF : then shall the base BC be equal to the base E ; and the tri- angle ABC to the triangle DEF ; B CE D and the other angles , to which the equal sides are oppo- site , shall be equal , each to ...
Página 30
... angle BDC greater than the angle BCD . Again , be- cause CB is equal to DB , the angle BDC is equal to the angle BCD ... BAC is equal to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on ...
... angle BDC greater than the angle BCD . Again , be- cause CB is equal to DB , the angle BDC is equal to the angle BCD ... BAC is equal to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on ...
Página 31
... angle BAC coincides with the an- gle EDF , and is equal to it . Therefore if two trian- gles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be the given ...
... angle BAC coincides with the an- gle EDF , and is equal to it . Therefore if two trian- gles , & c . Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be the given ...
Página 36
... angles . Let ABC be a triangle , and let its side BC be pro- duced to D , the exterior angle ACD is greater than ei- ther of the interior oppo- site angles CBA , BAC . Bisecta AC in E , join BE and produce it to F , and make EF equal to ...
... angles . Let ABC be a triangle , and let its side BC be pro- duced to D , the exterior angle ACD is greater than ei- ther of the interior oppo- site angles CBA , BAC . Bisecta AC in E , join BE and produce it to F , and make EF equal to ...
Página 37
... angle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ... BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII .
... angle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ... BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII .
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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.