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 |
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Αποτελέσματα 1 - 5 από τα 32.
Σελίδα 12
... 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 other angles shall ...
... 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 other angles shall ...
Σελίδα 13
... sides be produced , the angles upon the other side of the base shall be equal . B G D E Steps of the Demonstration . [ base BG = base CF 1. Prove that in △ AGB ABGACF of A AFC , AGB AFC 2 . that BF CG , 3 . that V BCFCBG , 4 . and BCG ...
... sides be produced , the angles upon the other side of the base shall be equal . B G D E Steps of the Demonstration . [ base BG = base CF 1. Prove that in △ AGB ABGACF of A AFC , AGB AFC 2 . that BF CG , 3 . that V BCFCBG , 4 . and BCG ...
Σελίδα 15
... side of it , there cannot be two 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 ...
... side of it , there cannot be two 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 ...
Σελίδα 16
... sides of the one shall be equal to the angle contained by the two sides , equal to them , of the other . B D E Steps of the Demonstration . Conceiving the A s applied to each other as directed , 1. Prove that the point c coincides with ...
... sides of the one shall be equal to the angle contained by the two sides , equal to them , of the other . B D E Steps of the Demonstration . Conceiving the A s applied to each other as directed , 1. Prove that the point c coincides with ...
Σελίδα 18
... side of it , are either two right angles , or are together equal to two right angles . Fig . 1 . A Fig . 2 . E ... sides of it make the adjacent angles together equal to two right angles , these two straight lines shall be in one ...
... side of it , are either two right angles , or are together equal to two right angles . Fig . 1 . A Fig . 2 . E ... sides of it make the adjacent angles together equal to two right angles , these two straight lines shall be in one ...
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.