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 |
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Resultat 1-5 av 12
Side 9
... described to be the inclination , that is , the degree of increasing width or separation , between the lines which form it , and does not at all depend on the length of those lines . This will be readily understood by an example . Let a ...
... described to be the inclination , that is , the degree of increasing width or separation , between the lines which form it , and does not at all depend on the length of those lines . This will be readily understood by an example . Let a ...
Side 37
... described upon the side subtending the right angle , is equal to the squares de- scribed upon the sides which contain the right angle . B D G E H K In the construction of the figure it is necessary to show that GA is on the same right ...
... described upon the side subtending the right angle , is equal to the squares de- scribed upon the sides which contain the right angle . B D G E H K In the construction of the figure it is necessary to show that GA is on the same right ...
Side 38
Euclides. PROPOSITION XLVIII . Theorem . If the square described on one side of a triangle be equal to the squares described upon the other two ; the angle contained by these two sides is a right angle . D B Steps of the Demonstration ...
Euclides. PROPOSITION XLVIII . Theorem . If the square described on one side of a triangle be equal to the squares described upon the other two ; the angle contained by these two sides is a right angle . D B Steps of the Demonstration ...
Side 39
... described , it is evident that since BC is 3 inches long , the whole figure may be divided into 3 rows , each con- taining 5 square inches ; in other words , the area of the figure is equal to 3 times 5 square inches , or is equal to ...
... described , it is evident that since BC is 3 inches long , the whole figure may be divided into 3 rows , each con- taining 5 square inches ; in other words , the area of the figure is equal to 3 times 5 square inches , or is equal to ...
Side 68
... described that DA , DB , DC each other ; and .. a with centre D and one of these lines as distance , will pass through the extremities of the other two . Steps of the Demonstration to Case 2nd , In which ABD ‡ △ BAD . 1. Prove that AE ...
... described that DA , DB , DC each other ; and .. a with centre D and one of these lines as distance , will pass through the extremities of the other two . Steps of the Demonstration to Case 2nd , In which ABD ‡ △ BAD . 1. Prove that AE ...
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.