## The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |

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### Common terms and phrases

abcd adjacent angles angle abc angle acb angle agh angle bac angle bcd angle dbe angle edf angle equal angles cab base bc bc is equal bisect centre circle abc circumference diameter double draw a straight equal angles equal circles equal straight lines equal to fb EUCLID'S ELEMENTS exterior angle fore given point given rectilineal angle given straight line gnomon greater half a right hypotenuse isosceles triangle less Let abc Let the straight line be drawn opposite angles parallel parallelogram perpendicular point f Prob produced Q. E. D. Prop rectangle ae rectangle contained rectilineal figure remaining angle right angles segment semicircle side bc square of ac straight line ac straight line drawn Theor touches the circle trapezium triangle abc twice the rectangle vertex vertical angle

### Popular passages

Page 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 20 - If two triangles have two sides of the one equal to two sides of the...

Page 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.

Page 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.

Page 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; 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 of the line which meets it, the line which meets it shall touch the circle.

Page 82 - 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.

Page 11 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

Page 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.

Page 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.