# 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

John W. Parker, 1837 - 88 ůŚŽŖšŚÚ
0  ŮťŰťÍ›Ú
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### ‘ť Ž›ŪŚ Ôť ųŮřůŰŚÚ -”żŪŰŠÓÁ ÍŮťŰťÍřÚ

ńŚŪ ŚŪŰÔūŖůŠžŚ ÍŮťŰťÍ›Ú ůŰťÚ ůűŪřŤŚťÚ ŰÔūÔŤŚůŖŚÚ.

### –ŚŮťŚųŁžŚŪŠ

 ŇŪŁŰÁŰŠ 1 1 ŇŪŁŰÁŰŠ 2 5 ŇŪŁŰÁŰŠ 3 9 ŇŪŁŰÁŰŠ 4 11 ŇŪŁŰÁŰŠ 5 17 ŇŪŁŰÁŰŠ 6 18 ŇŪŁŰÁŰŠ 7 23 ŇŪŁŰÁŰŠ 8 33
 ŇŪŁŰÁŰŠ 9 36 ŇŪŁŰÁŰŠ 10 38 ŇŪŁŰÁŰŠ 11 47 ŇŪŁŰÁŰŠ 12 49 ŇŪŁŰÁŰŠ 13 65 ŇŪŁŰÁŰŠ 14 79 ŇŪŁŰÁŰŠ 15 84

### ńÁžÔŲťŽř ŠūÔůū‹ůžŠŰŠ

”ŚŽŖšŠ 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...
”ŚŽŖšŠ 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.
”ŚŽŖšŠ 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.
”ŚŽŖšŠ 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...
”ŚŽŖšŠ 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.
”ŚŽŖšŠ 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.
”ŚŽŖšŠ 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.
”ŚŽŖšŠ 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.
”ŚŽŖšŠ 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.