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, Elements of Plane and Spherical TrigonometryMarot & Walter, 1826 - 320 pagine |
Dall'interno del libro
Risultati 1-5 di 57
Pagina 83
... segments between the point ' and the extremities of the base is equal to the difference between the square of the line drawn ' to the opposite angle , and the square of one of the equal sides . 6 6 6 ' Let ABC be an isosceles triangle ...
... segments between the point ' and the extremities of the base is equal to the difference between the square of the line drawn ' to the opposite angle , and the square of one of the equal sides . 6 6 6 ' Let ABC be an isosceles triangle ...
Pagina 86
... segment of a circle is the figure contained by a straight line , and the arch which it cuts off . VI . An angle in a segment is the angle contained by two straight lines drawn from any point in the cir- cumference of the segment , to ...
... segment of a circle is the figure contained by a straight line , and the arch which it cuts off . VI . An angle in a segment is the angle contained by two straight lines drawn from any point in the cir- cumference of the segment , to ...
Pagina 105
... segment of a circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED : The an- gles BAD , BED are equal to one another . Take F the centre of the circle ABCD : And , first , let the seg ...
... segment of a circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED : The an- gles BAD , BED are equal to one another . Take F the centre of the circle ABCD : And , first , let the seg ...
Pagina 106
... segment BAED be not greater than a se- micircle , let BAD , BED be an- gles in it ; these also are equal to one another . Draw AF to the centre , and produce it to C , and B join CE : Therefore the segment BADC is greater than a semicir ...
... segment BAED be not greater than a se- micircle , let BAD , BED be an- gles in it ; these also are equal to one another . Draw AF to the centre , and produce it to C , and B join CE : Therefore the segment BADC is greater than a semicir ...
Pagina 107
... segments must there- fore fall within the other : let ACB fall within ADB , draw the straight line BCD , and join CA , DA : and because the segment ACB is simi- lar to the segment ADB , and similar segments of circles contain equal ...
... segments must there- fore fall within the other : let ACB fall within ADB , draw the straight line BCD , and join CA , DA : and because the segment ACB is simi- lar to the segment ADB , and similar segments of circles contain equal ...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Visualizzazione completa - 1826 |
Parole e frasi comuni
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected Book centre circle ABC circumference cosine cylinder demonstrated described diameter draw drawn equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line gles greater hypotenuse inscribed join less Let ABC line BC magnitudes meet opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB proportional proposition pyramid Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle right angled triangle segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line AC Supplement THEOR third touches the circle triangle ABC triangle DEF wherefore
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Pagina 233 - But because the triangle KGN is isosceles, the angle GKN is equal to the angle GNK, and the angles GMK, GMN are both right angles by construction ; wherefore, the triangles GMK, GMN have two angles of the one equal to two angles of the other, and they have also the side GM common, therefore they
Pagina 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it. VIII. An obtuse angle is that which is greater than a right angle.
Pagina 77 - AB is divided in H, so that the rectangle AB, BH is equal to the square of AH. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal
Pagina 69 - line be divided into two equal parts* and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square of the line between the points of section., is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the
Pagina 48 - PROP. XXX. THEOR. Straight lines which are parallel to the same straight line are parallel to one another. Let AB, CD, be each of them parallel to EF; AB is also parallel to CD. Let the straight line GHK cut AB, EF, CD ; and because GHK cuts the parallel straight lines
Pagina 32 - PROP. XI. PROB. To draw a straight line at right angles to a given straight line, from a given point in that line. Let AB be a given straight line, and Ca point given in it; it is required to draw a straight line from the point C at right angles to AB.
Pagina 75 - PROP. X. THEOR. If a straight line be bisected, and produced to any point, the square* of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half
Pagina 18 - taken, the straight line between them lies wholly in that superficies. VI. 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. E NB ' When several angles are at one point B, any one of them is
Pagina 153 - Therefore, &c. QED PROP. IV. THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of the first and third, and any whatever of the second and fourth; the multiple
Pagina 50 - angles. Therefore, twice as many right angles as the figure has sides, are equal to all the angles of the figure, together with four right angles, that is, the angles of the figure are equal to twice as many right angles as the figure has sides, wanting four. Because every interior angle ABC, with its adjacent exterior ABD, is