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 σελίδες |
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Σελίδα ix
... manner , the quadrature of the circle is performed only by approximation , or by finding two rectangles nearly equal to one another ; one of them greater , and another less than the space contained within the circle . In the Second Book ...
... manner , the quadrature of the circle is performed only by approximation , or by finding two rectangles nearly equal to one another ; one of them greater , and another less than the space contained within the circle . In the Second Book ...
Σελίδα x
... manner of doing which he has not previously explained . Now , the only use of this rule is to prevent the admission of im- possible or contradictory suppositions , which , no doubt , might lead into error ; and it is a rule well ...
... manner of doing which he has not previously explained . Now , the only use of this rule is to prevent the admission of im- possible or contradictory suppositions , which , no doubt , might lead into error ; and it is a rule well ...
Σελίδα xii
... manner of actually de scribing them may not have been explained . In this way , I have been enabled to offer that very refined artifice in geometrical reasoning , to which we give the name of the Method of Exhaustions , under a much ...
... manner of actually de scribing them may not have been explained . In this way , I have been enabled to offer that very refined artifice in geometrical reasoning , to which we give the name of the Method of Exhaustions , under a much ...
Σελίδα 35
... manner it may be 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 ...
... manner it may be 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 ...
Σελίδα 36
... manner , if the side BC be bisected , it may be 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 ...
... manner , if the side BC be bisected , it may be 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 ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 26 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 54 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 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.