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

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Side 10

**Q. E. D.**COROLLARY . Hence every equilateral triangle is also equiangular .**PROP**. VI . THEOR . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal ... Side 11

**Q. E. D. PROP**. VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be equal to ... Side 12

**Q. E. D. PROP**. IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let Bac be the given rectilineal angle , it is required to bisect it . Take any point p in AB , and from ac cut ( 1. 3. ) ... Side 15

**Q.E.D. PROP**. XIV . THEOR . 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 ... Side 16

**Q. E. D.**Cor . 1. From this it is manifest , that , if two straight lines cut one another , the angles they make at the ... F**PROP**. XVI . THEOR . If one side of a triangle be produced , the exterior angle is greater than either of the ...### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

ABCD angle ABC angle ACB angle BAC angle equal base BC BC is equal bisect centre circle ABC circumference coincide common construct demonstrated describe diameter divided double draw equal angles equal to FB equilateral exterior angle extremity figure fore four given point given straight line gnomon greater impossible interior isosceles triangle join less Let ABC likewise line be drawn lines AC meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced PROP Q.E.D. PROP rectangle contained remaining angle right angles segment semicircle shown sides squares of AC straight line A B Take taken THEOR third touch touches the circle triangle ABC twice the rectangle vertex wherefore whole

### Populære avsnitt

Side 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...

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

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

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

Side 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.

Side 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.

Side 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.

Side 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.

Side 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.

Side 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.