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 graduate
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AD X DC ae x ec angle contained angle equal Argument ad absurdum bc x cd bisect cuts the circle Demonstration itself consists described with centre diameter Engravings equal straight lines equi equiangular equilateral fall figure given circle given point given rectilineal angle given straight line given triangle i. e. less inscribe interior angles learner line be divided line drawn line touches parallel parallelogram pass pentagon point of contact Problem proof Proposition IV Proposition VIII Proposition XV Prove that Zs Proved by showing rectangle contained right angles right line right Zs shows the supposition similarly Steps subtending Suppose supposition is false Theorem whole line Zs abc
الصفحة 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...
الصفحة 89 - THERE is a wisdom in this beyond the rules of physic ; a man's own observation, what he finds good of, and what he finds hurt of, is the best physic to preserve health. But it is a safer conclusion to say, " This agreeth not well with me, therefore I will not continue it," than this, " I find no offence of this, therefore I may use it.
الصفحة 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.
الصفحة 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...
الصفحة 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.
الصفحة 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.
الصفحة 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.
الصفحة 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.
الصفحة 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.