## 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 11

and

BC is common to both triangles , the two sides DB , B Care equal to the two sides

AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; ( hyp . ) ...

and

**join**DC . Then , in the triangles DBC , ABC , because DB is equal to AC , andBC is common to both triangles , the two sides DB , B Care equal to the two sides

AC , CB , each to each ; and the angle DBC is equal to the angle ACB ; ( hyp . ) ...

Side 30

The straight lines which

lines towards the same parts , are also ...

to CD , and BC meets them , therefore the angle ABC is equal to the alternate

angle ...

The straight lines which

**join**the extremities of two equal and parallel straightlines towards the same parts , are also ...

**Join**BC . Then because AB is parallelto CD , and BC meets them , therefore the angle ABC is equal to the alternate

angle ...

Side 35

D А B C E F

BF , if possible , through A draw À G parallel to BF , ( 1 . 31 . ) meeting ED , or ED

produced in G , and

D А B C E F

**Join**AD ; then AD shall be parallel to BF . For if AD be not parallel toBF , if possible , through A draw À G parallel to BF , ( 1 . 31 . ) meeting ED , or ED

produced in G , and

**join**ĞF . Then the triangle ABC is equal to the triangle GEF ... Side 40

and

the angle BAG is a right angle , ( def . 30 . ) the two straight lines AC , AG upon

the opposite sides of AB , make with it at the point A , the adjacent angles equal ...

and

**join**AD , FC . Then because the angle BAC is a right angle , ( hyp . ) and thatthe angle BAG is a right angle , ( def . 30 . ) the two straight lines AC , AG upon

the opposite sides of AB , make with it at the point A , the adjacent angles equal ...

Side 58

of the square BG , and KH produced meets CE in E . Let LA meet BC ' in M .

DA ; then the square GB and the oblong LB are each double of the triangle DAB ,

( Euc . 1 . 41 . ) ; and similarly by

of the square BG , and KH produced meets CE in E . Let LA meet BC ' in M .

**Join**DA ; then the square GB and the oblong LB are each double of the triangle DAB ,

( Euc . 1 . 41 . ) ; and similarly by

**joining**EA , the square HC and oblong LC are ...### Hva folk mener - Skriv en omtale

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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.