## 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 88

Side 6

THINGS which are

be added to

the remainders are

THINGS which are

**equal**to the same thing are**equal**to one another . II . If**equals**be added to

**equals**, the wholes are**equal**. III . If**equals**be taken from**equals**,the remainders are

**equal**. IV . If**equals**be added to unequals , the wholes are ... Side 8

Then the straight line AL shall be

of the circle CGH , therefore BC is

center of the circle GKL , therefore DL is

...

Then the straight line AL shall be

**equal**to BC . Because the point B is the centerof the circle CGH , therefore BC is

**equal**to BG ; ( def . 15 . ) and because D is thecenter of the circle GKL , therefore DL is

**equal**to DG , and DA , DB parts of them...

Side 9

Then shall the base BC be

triangle DEF ; and the other angles to which the

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 ACBto ...

Side 10

therefore the base FC is

remaining angles of the other , each to each , to which the

opposite ...

therefore the base FC is

**equal**to the base GB , ( I . 4 . ) and the triangle AFC is**equal**to the triangle AGB , also the remaining angles of the one are**equal**to theremaining angles of the other , each to each , to which the

**equal**sides areopposite ...

Side 11

For , if AB be not

let AB be greater than AC ; and from BA cut off BD

and join DC . Then , in the triangles DBC , ABC , because DB is

For , if AB be not

**equal**to AC , one of them is greater than the other . If possible ,let AB be greater than AC ; and from BA cut off BD

**equal**to CA the less , ( 1 . 3 . )and join DC . Then , in the triangles DBC , ABC , because DB is

**equal**to AC ...### 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.