## 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

Resultat 1-5 av 73

Side 113

... parallel to EB meeting AB in F . Then AB is divided in F , so that the rectangle

AF , FB is equal to the square on M . ( 11 . 14 . ) The square will be the greatest ,

when ED

... parallel to EB meeting AB in F . Then AB is divided in F , so that the rectangle

AF , FB is equal to the square on M . ( 11 . 14 . ) The square will be the greatest ,

when ED

**touches**the semicircle , or when M is equal to half of the given line AB . Side 120

A straight line is said to

produced does not cut it . III . Circles are said to

but do not cut one another . IV . Straight lines are said to be equally distant from

the ...

A straight line is said to

**touch**a circle when it meets the circle , and beingproduced does not cut it . III . Circles are said to

**touch**one another , which meet ,but do not cut one another . IV . Straight lines are said to be equally distant from

the ...

Side 125

Let the circle CDE

have the same center . RE If possible , let F be the center of the two circles : join

FC , and draw any straight line FEB , meeting the circumferences in Eand B . And

...

Let the circle CDE

**touch**the circle ABC internally in the point C . They shall nothave the same center . RE If possible , let F be the center of the two circles : join

FC , and draw any straight line FEB , meeting the circumferences in Eand B . And

...

Side 130

If one circle

their centers being produced , shall pass through that point of contact . Let the

circle ADE

the ...

If one circle

**touch**another internally in any point , the straight line which joinstheir centers being produced , shall pass through that point of contact . Let the

circle ADE

**touch**the circle ABC internally in the point A ; and let F be the center ofthe ...

Side 131

THEOREM . One circle cannot

it

THEOREM . One circle cannot

**touch**another in more points than in one , whetherit

**touches**it on the inside or outside . For , if it be possible , let the circle EBF**touch**the circle ABC in more points than in one . and first on the ...### 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.