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 6-10 av 26
Side 20
... less than two right angles . Steps of the Demonstration . 1. Prove that ZS DCA + ACB > < S ACB + CBA , that LS ACB + CBA < 2 right Ls , 2 . 3 . that similarly each of the other pairs of Ls is 2 right Ls . PROPOSITION XVIII . Theorem ...
... less than two right angles . Steps of the Demonstration . 1. Prove that ZS DCA + ACB > < S ACB + CBA , that LS ACB + CBA < 2 right Ls , 2 . 3 . that similarly each of the other pairs of Ls is 2 right Ls . PROPOSITION XVIII . Theorem ...
Side 22
... less than the other two sides of the triangle , but shall con- tain a greater angle . Steps of the Demonstration . 1. Prove that BA + AC > BE + EC , that BE + EC > CD + DB , that much more is BA + AC > CD + Db , 2 . 3 . 4 . that BDC ...
... less than the other two sides of the triangle , but shall con- tain a greater angle . Steps of the Demonstration . 1. Prove that BA + AC > BE + EC , that BE + EC > CD + DB , that much more is BA + AC > CD + Db , 2 . 3 . 4 . that BDC ...
Side 25
... less = greater ; which shows the supposition to be false ; and : . that AB DE , 3. that in As ABC , DEF base AC base DF , and LBAC EDF . B H C E Steps of the Demonstration to Case 2nd . Suppose that BC EF , and that a part of BC , as BH ...
... less = greater ; which shows the supposition to be false ; and : . that AB DE , 3. that in As ABC , DEF base AC base DF , and LBAC EDF . B H C E Steps of the Demonstration to Case 2nd . Suppose that BC EF , and that a part of BC , as BH ...
Side 28
... less than two right angles , these right lines being continually produced , shall at length meet on that side on which are the angles which are less than two right angles . " Let the right line EF meet the two right lines AB , CD ; and ...
... less than two right angles , these right lines being continually produced , shall at length meet on that side on which are the angles which are less than two right angles . " Let the right line EF meet the two right lines AB , CD ; and ...
Side 33
... , prove , 1. that △ ABC = △ EBC , 2. that △ EBC △ DBC , i . e . , less greater , which shows the supposition to be false , 3. that . AD || BC . C PROPOSITION XL . ( Argument ad absurdum . ) Theorem FIRST BOOK . 33.
... , prove , 1. that △ ABC = △ EBC , 2. that △ EBC △ DBC , i . e . , less greater , which shows the supposition to be false , 3. that . AD || BC . C PROPOSITION XL . ( Argument ad absurdum . ) Theorem FIRST BOOK . 33.
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.