## The school edition. Euclid's Elements of geometry, the first six books, by R. Potts. corrected and enlarged. corrected and improved [including portions of book 11,12]. |

### Inni boken

Side 8

... have the two sides AB , AC equal to the two sides DE , DF , each to each , viz .

AB to DE , and AC to DF , and the included angle BAC equal to the included

angle EDF . Then shall the base BC be equal to the base

.

... have the two sides AB , AC equal to the two sides DE , DF , each to each , viz .

AB to DE , and AC to DF , and the included angle BAC equal to the included

angle EDF . Then shall the base BC be equal to the base

**EUCLID**' S ELEMENTS.

Side 10

... are opposite to , the equal angles , shall be equal to one another . Let ABC be

a triangle having the angle ABC ' equal to the angle ACB . Then the side AB shall

be equal to the side AC . For , if AB be not equal to AC ,

... are opposite to , the equal angles , shall be equal to one another . Let ABC be

a triangle having the angle ABC ' equal to the angle ACB . Then the side AB shall

be equal to the side AC . For , if AB be not equal to AC ,

**EUCLID**' S ELEMENTS . Side 22

... to the two DE , DF , each to each , namely , AB equal to DE , and AC to DF ; but

the angle BAC greater than the angle EDF . Then the base B C shall be greater

than the base EF . · Of the two sides DE , DF , let 22

... to the two DE , DF , each to each , namely , AB equal to DE , and AC to DF ; but

the angle BAC greater than the angle EDF . Then the base B C shall be greater

than the base EF . · Of the two sides DE , DF , let 22

**EUCLID**' S ELEMENTS . Side 30

and the triangle ABC to the triangle BCD , and the other angles to the other

angles , each 30

and the triangle ABC to the triangle BCD , and the other angles to the other

angles , each 30

**EUCLID**' S ELEMENTS . Side 38

... equal to two right angles ; ( I . 29 . ) therefore also the angles HGF , HGL are

equal to two right angles , and therefore FG is in the same straight line with GL . (

1 . 14 . ) And because KF is parallel to HG , and HG 33

... equal to two right angles ; ( I . 29 . ) therefore also the angles HGF , HGL are

equal to two right angles , and therefore FG is in the same straight line with GL . (

1 . 14 . ) And because KF is parallel to HG , and HG 33

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### Vanlige uttrykk og setninger

ABCD Algebraically Apply base bisected Book chord circle circumference common construction contained definition demonstrated described diagonals diameter difference distance divided double draw drawn equal equal angles equiangular equilateral triangle equimultiples Euclid extremities fall figure formed four fourth Geometrical given circle given line given point given straight line greater half Hence inscribed intersection isosceles join length less Let ABC line drawn magnitudes manner mean meet multiple parallel parallelogram pass perpendicular plane problem produced Prop proportionals proved Q.E.D. PROPOSITION radius ratio reason rectangle rectangle contained regular remaining respectively right angles segment semicircle shew shewn sides similar solid square straight line taken tangent THEOREM third touch triangle ABC twice units vertex wherefore whole

### Populære avsnitt

Side 112 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.

Side 83 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...

Side 48 - If two triangles have two sides of the one equal to two sides of the other, each to each ; and...

Side 238 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Side 198 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater, that is, ' when the less is contained a certain number of times exactly in the greater.

Side 271 - SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.

Side 81 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 115 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.

Side 341 - On the same base, and on the same side of it, there cannot be two triangles...

Side 24 - ... twice as many right angles as the figure has sides ; therefore all the angles of the figure together with four right angles, are equal to twice as many right angles as the figure has sides.