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 27
... demonstrated . PROP . V. THEOR . The angles at the base of an Isosceles triangle N are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an Isosceles triangle N are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . Let ABC be an isosceles ...
Página 35
... demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. b PROP . XV . THEOR . ? * ? " If two straight lines cut one ...
... demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. b PROP . XV . THEOR . ? * ? " If two straight lines cut one ...
Página 36
... demonstrated that the angle BCG , that is " , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c . Q. E. D. PROP . XVII . THEOR . Any treo angles of a triangle are together less than two right angles . Book I ...
... demonstrated that the angle BCG , that is " , the angle ACD , is greater than the angle ABC . Therefore , if one side , & c . Q. E. D. PROP . XVII . THEOR . Any treo angles of a triangle are together less than two right angles . Book I ...
Página 37
... demonstrated , that BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII . THEOR . The greater side of every triangle has the greater angle opposite to it . Let ABC ...
... demonstrated , that BAC , ACB , as also , CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII . THEOR . The greater side of every triangle has the greater angle opposite to it . Let ABC ...
Página 39
... demonstrated , that the sides AB , BC are greater than CA , and BC CA greater than AB . Therefore any two sides , & c . Q. E. D. PROP . XXI . THEOR . If from the ends of one side of a triangle , there be drawn two straight lines to a ...
... demonstrated , that the sides AB , BC are greater than CA , and BC CA greater than AB . Therefore any two sides , & c . Q. E. D. PROP . XXI . THEOR . If from the ends of one side of a triangle , there be drawn two straight lines to a ...
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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.