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 |
Inni boken
Resultat 1-5 av 25
Side 49
... centre of a given circle . D B E Steps of the Demonstration . Suppose that F is not in the centre of the O , but that some other point , as G , is the centre . Then prove , on that supposition , they are both rights , 1. that ( in AS ...
... centre of a given circle . D B E Steps of the Demonstration . Suppose that F is not in the centre of the O , but that some other point , as G , is the centre . Then prove , on that supposition , they are both rights , 1. that ( in AS ...
Side 50
... centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and if it cuts it at right angles , it shall bisect it . F D B Part 1st is proved ( from viii . 1. ) 50 THIRD BOOK .
... centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and if it cuts it at right angles , it shall bisect it . F D B Part 1st is proved ( from viii . 1. ) 50 THIRD BOOK .
Side 51
... centre , they do not bisect each other . Steps of the Demonstration . Suppose that AC , BD do bisect each other in E. ( State that this is evidently impossible if one line pass through the centre , and the other not ) . If neither of ...
... centre , they do not bisect each other . Steps of the Demonstration . Suppose that AC , BD do bisect each other in E. ( State that this is evidently impossible if one line pass through the centre , and the other not ) . If neither of ...
Side 52
... centre . Suppose that F is the centre of both Os ; and prove , on that supposition , that FE and FB each = Fc , and each other ; i . e . less greater , which shows the supposition to be false . PROPOSITION VII . B Theorem . If a point ...
... centre . Suppose that F is the centre of both Os ; and prove , on that supposition , that FE and FB each = Fc , and each other ; i . e . less greater , which shows the supposition to be false . PROPOSITION VII . B Theorem . If a point ...
Side 53
... centre is , and the other part of that dia- meter is the least ; and of any others , that which is the nearest to the line which passes through the centre , is always greater than C the more remote : and from the same point only two ...
... centre is , and the other part of that dia- meter is the least ; and of any others , that which is the nearest to the line which passes through the centre , is always greater than C the more remote : and from the same point only two ...
Vanlige uttrykk og setninger
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 avsnitt
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.