A companion to Euclid: being a help to the understanding and remembering of the first four books. With a set of improved figures, and an original demonstration of the proposition called in Euclid the twelfth axiom, by a graduateJohn W. Parker, 1837 - 88 sider |
Fra bogen
Side 8
... for a parallelogram than simply O. In the Second Book the reader will find an explanation of the symbol AB X CD , as used for the rectangle contained by AB and CD . how one angle is said to be greater or less 8 PRELIMINARY OBSERVATIONS.
... for a parallelogram than simply O. In the Second Book the reader will find an explanation of the symbol AB X CD , as used for the rectangle contained by AB and CD . how one angle is said to be greater or less 8 PRELIMINARY OBSERVATIONS.
Side 40
... the other three Books ; and he will find it an important assistance carefully to com- mit to memory the enunciations of all ... one of which is di- vided into any number of parts , the rectangle contained by the two straight lines is equal to ...
... the other three Books ; and he will find it an important assistance carefully to com- mit to memory the enunciations of all ... one of which is di- vided into any number of parts , the rectangle contained by the two straight lines is equal to ...
Side 41
... a straight line be divided into any two B parts , the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two parts , together with the square of the aforesaid part . D E Proved by showing ...
... a straight line be divided into any two B parts , the rectangle contained by the whole and one of the parts is equal to the rectangle contained by the two parts , together with the square of the aforesaid part . D E Proved by showing ...
Side 43
... a straight line be di vided into any two parts , the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole line and that part , together with the square of the other part . A K H D F ...
... a straight line be di vided into any two parts , the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole line and that part , together with the square of the other part . A K H D F ...
Side 45
... whole line thus . produced , and the square of the part of it produced , are ... a rt . 4 , 1. that S BEF + EFD < 2 rt . Zs , in order to prove that EB , FD ... parts , so that the rectangle contained by the whole and one of the parts ...
... whole line thus . produced , and the square of the part of it produced , are ... a rt . 4 , 1. that S BEF + EFD < 2 rt . Zs , in order to prove that EB , FD ... parts , so that the rectangle contained by the whole and one of the parts ...
Almindelige termer og sætninger
AB² AC² AD² AEX EC angle contained angle equal Argument ad absurdum base DF BC² BD² bisect CB² cuts the circle DC² Demonstration itself consists diameter EB² EF² EG² Engravings equal straight lines equi equiangular equilateral Euclid F Steps fall figure GF² given circle given point given rectilineal angle given straight line given triangle i. e. less inscribe interior angles learner less greater line be divided line drawn parallel parallelogram PARKER pass pentagon point of contact Problem proof PROPOSITION IX PROPOSITION VIII Proved by showing rectangle contained right angles right line shows the supposition similarly Suppose supposition is false Theorem WEST STRAND whole line
Populære passager
Side 24 - If two triangles have two angles of the [one equal to two angles of the other, each to each, and one side equal to one side, namely, either t}le sides adjacent to the equal...
Side 45 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Side 18 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 61 - From this it is manifest that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it, touches the circle...
Side 37 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 76 - 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.
Side 77 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it, and if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on GEOMETRY.
Side 72 - If a straight line touch a circle, and from the point of contact a straight line be drawn at right angles to the touching line, the centre of the circle shall be in that line.
Side 27 - If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite angle on the same side; and also the two interior angles on the same side together equal to two right angles.