Euclid Revised: Containing the Essentials of the Elements of Plane Geometry as Given by Euclid in His First Six Books, with Numerous Additional Propositions and ExercisesClarendon Press, 1890 - 400 sider |
Inni boken
Resultat 1-5 av 53
Side 126
... touch ) at a point , when they meet at that point without cutting each other . Ax . If two circles touch , one must be wholly within , or wholly without the other . Def . When two circles are in contact , so that one is wholly within ...
... touch ) at a point , when they meet at that point without cutting each other . Ax . If two circles touch , one must be wholly within , or wholly without the other . Def . When two circles are in contact , so that one is wholly within ...
Side 135
... centres passes through the point of contact of the circles : this assumes iii . 13 . Note ( 2 ) The converses of Props . 11 and 12 will be found in the Addenda . Proposition 13 . THEOREM - Two circles cannot touch in BOOK iii . 135.
... centres passes through the point of contact of the circles : this assumes iii . 13 . Note ( 2 ) The converses of Props . 11 and 12 will be found in the Addenda . Proposition 13 . THEOREM - Two circles cannot touch in BOOK iii . 135.
Side 136
... touch in more than one point . Let O , C be the centres of two Os in contact : then OC , the line of centres , passes through a pt . of contact - say P. Assume Q to be another pt . of cont . Join OQ , CQ . 1o , let the contact be ...
... touch in more than one point . Let O , C be the centres of two Os in contact : then OC , the line of centres , passes through a pt . of contact - say P. Assume Q to be another pt . of cont . Join OQ , CQ . 1o , let the contact be ...
Side 138
... . on ON , sq . on AM > sq . on CN ; or AM > CN : i . e . AB > CD . And ( y ) , if AB > CD , then AM > CN , so that sq . on AM > sq . on CN , sq . on OM < sq . on ON . ... OM < ON . Def . A straight line is said to touch , 138 EUCLID.
... . on ON , sq . on AM > sq . on CN ; or AM > CN : i . e . AB > CD . And ( y ) , if AB > CD , then AM > CN , so that sq . on AM > sq . on CN , sq . on OM < sq . on ON . ... OM < ON . Def . A straight line is said to touch , 138 EUCLID.
Side 139
... touch , or be a tangent to a circle , if the line meets the circle , but does not , when produced , cut it . Proposition 16 . THEOREM - In a circle- ( a ) a straight line perpendicular to a diameter at one of its extremities touches the ...
... touch , or be a tangent to a circle , if the line meets the circle , but does not , when produced , cut it . Proposition 16 . THEOREM - In a circle- ( a ) a straight line perpendicular to a diameter at one of its extremities touches the ...
Vanlige uttrykk og setninger
ABCD Addenda altitude base bisector bisects centre of similitude chord circum-circle circumf circumference coincide collinear concyclic corners cross-ratio cyclic quadrilateral diag diagonals diam diameter divided draw drawn equal angles equiang Euclid find the Locus fixed circle fixed line fixed point given circle given line given point harmonic conjugates inscribed intersection inverse Join Let ABC magnitudes meet mid point mid pt Note-The NOTE-Use opposite sides pair parallel parallelogram pedal triangle perpendicular polygon PROBLEM-To produced Prop Proposition Proposition 13 Ptolemy's Theorem quad radical axis radii radius ratio rect rectangle rectilineal figure respectively right angles segments segt Similarly simr Simson's Line square straight line tang tangents THEOREM THEOREM-If touch triangle ABC variable
Populære avsnitt
Side 251 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 29 - 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, viz.
Side 150 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Side 91 - 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 on the other part.
Side 82 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 37 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Side 44 - 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.
Side 84 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 22 - Any two sides of a triangle are together greater than the third side.
Side 87 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...