## 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]. |

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Resultat 1-5 av 83

Side 7

Then

the circle BCD , therefore AC is equal to AB ; ( def . 15 . ) and because the point B

is the center of the circle ACE , therefore B C is equal to AB ; but it has been ...

Then

**ABC**shall be an equilateral**triangle**. Because the point A is the center ofthe circle BCD , therefore AC is equal to AB ; ( def . 15 . ) and because the point B

is the center of the circle ACE , therefore B C is equal to AB ; but it has been ...

Side 9

Then shall the base BC be equal to the base EF ; and the

triangle DEF ; and the other angles to which the equal sides are opposite shall be

equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB

to ...

Then shall the base BC be equal to the base EF ; and the

**triangle ABC**to thetriangle DEF ; and the other angles to which the equal sides are opposite shall be

equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB

to ...

Side 10

and the triangle AFC is equal to the triangle AGB , also the remaining angles of

the one are equal to the remaining angles ... which are the angles at the base of

the

the ...

and the triangle AFC is equal to the triangle AGB , also the remaining angles of

the one are equal to the remaining angles ... which are the angles at the base of

the

**triangle ÅBČ**; and it has also been proved , that the angle FB Ĉ is equal tothe ...

Side 12

For , if the

straight line BC on EF ; then because BC is equal to EF , ( hyp . ) therefore the

point C shall coincide with the point F ; wherefore BC coinciding with EF , BA and

...

For , if the

**triangle ABC**be applied to DEF , so that the point B be on E , and thestraight line BC on EF ; then because BC is equal to EF , ( hyp . ) therefore the

point C shall coincide with the point F ; wherefore BC coinciding with EF , BA and

...

Side 13

Upon AB describe the equilateral

ACB by the straight line CD meeting AB in the point D . ( 1 . 9 . ) Then AB shall be

cut into two equal parts in the point D . Because AC is equal to CB , ( constr . ) ...

Upon AB describe the equilateral

**triangle ABC**; ( 1 . 1 . ) DB and bisect the angleACB by the straight line CD meeting AB in the point D . ( 1 . 9 . ) Then AB shall be

cut into two equal parts in the point D . Because AC is equal to CB , ( constr . ) ...

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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.