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 24
Side 11
Euclides. FIRST BOOK . PROPOSITION I. Problem . To describe an equilateral triangle upon a given finite straight line . K B D H PROPOSITION II . B E Problem . From a given point to draw a straight line equal to a given straight line ...
Euclides. FIRST BOOK . PROPOSITION I. Problem . To describe an equilateral triangle upon a given finite straight line . K B D H PROPOSITION II . B E Problem . From a given point to draw a straight line equal to a given straight line ...
Side 12
... triangles have two sides of the one equal to two sides of the other , each to each ; and have also the angles contained by those sides equal ; the bases or third sides of the triangles shall be equal ; as also the triangles ; and their ...
... triangles have two sides of the one equal to two sides of the other , each to each ; and have also the angles contained by those sides equal ; the bases or third sides of the triangles shall be equal ; as also the triangles ; and their ...
Side 13
... triangles in paper , and actually applying one to the other according to the directions in Euclid . PROPOSITION V. Theorem . The angles at the base of an isosceles triangle are equal ; and if the equal sides be produced , the angles ...
... triangles in paper , and actually applying one to the other according to the directions in Euclid . PROPOSITION V. Theorem . The angles at the base of an isosceles triangle are equal ; and if the equal sides be produced , the angles ...
Side 15
... triangles that have their sides terminated in one extremity of the base equal to each other , and likewise those terminated in the other extremity . E B B Suppose it possible that the two AS ACB , ADB , on the same base AB can have the ...
... triangles that have their sides terminated in one extremity of the base equal to each other , and likewise those terminated in the other extremity . E B B Suppose it possible that the two AS ACB , ADB , on the same base AB can have the ...
Side 16
Euclides. PROPOSITION VIII . Theorem . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle contained by the two sides of the one shall be equal to ...
Euclides. PROPOSITION VIII . Theorem . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle contained by the two sides of the one shall be equal to ...
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.