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 σελίδες |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 7
... Given points , lines , and angles are also distinguished by larger letters . The learner will find it serviceable to ... circle , then the smaller one , and so on ; and consider it immaterial with what part he began , so that his figure ...
... Given points , lines , and angles are also distinguished by larger letters . The learner will find it serviceable to ... circle , then the smaller one , and so on ; and consider it immaterial with what part he began , so that his figure ...
Σελίδα 49
... 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 ADG , BDG ) 2 ...
... 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 ADG , BDG ) 2 ...
Σελίδα 56
... circumference , that point is the centre of the circle . Steps of the Demonstration . DE G C B Suppose that D is not ... given each other , which shows the supposition to be false , and : . that D is the centre . PROPOSITION X ...
... circumference , that point is the centre of the circle . Steps of the Demonstration . DE G C B Suppose that D is not ... given each other , which shows the supposition to be false , and : . that D is the centre . PROPOSITION X ...
Σελίδα 62
... given point , either G without or in the circumference , which shall touch a given circle . D E B Part 1st . To draw a tangent to O BCD , from point A without it . Steps of the Demonstration . ( base DF base AB 62 THIRD BOOK .
... given point , either G without or in the circumference , which shall touch a given circle . D E B Part 1st . To draw a tangent to O BCD , from point A without it . Steps of the Demonstration . ( base DF base AB 62 THIRD BOOK .
Σελίδα 63
... given point D is on the of the O , is proved by Cor . to xvi . 3 . PROPOSITION XVIII . ( Argument ad absurdum ) . B D G I Theorem . If a straight line touches a circle , the straight line drawn from the centre to the point of contact ...
... given point D is on the of the O , is proved by Cor . to xvi . 3 . PROPOSITION XVIII . ( Argument ad absurdum ) . B D G I Theorem . If a straight line touches a circle , the straight line drawn from the centre to the point of contact ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.