## 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 38

Side 3

A

circumference cut off by the diameter . XIX . The center of a

with that of the circle . XX . Rectilineal figures are those which are contained by

straight ...

A

**semicircle**is the figure contained by a diameter and the part of thecircumference cut off by the diameter . XIX . The center of a

**semicircle**is the samewith that of the circle . XX . Rectilineal figures are those which are contained by

straight ...

Side 44

Proclus remarks on this definition : “ Hence you may collect that the center has

three places : for it is either within the figure , as in the circle ; or in its perimeter ,

as in the

Proclus remarks on this definition : “ Hence you may collect that the center has

three places : for it is either within the figure , as in the circle ; or in its perimeter ,

as in the

**semicircle**; or without the figure , as in certain conic lines . ” Def . xx ! Side 98

from the center G , at the distance GB , or GF , describe the

produce DE to meet the circumference in H . The square described upon EH

shall be equal to the given rectilineal figure A . Join GH . Then because the

straight ...

from the center G , at the distance GB , or GF , describe the

**semicircle**BHF , andproduce DE to meet the circumference in H . The square described upon EH

shall be equal to the given rectilineal figure A . Join GH . Then because the

straight ...

Side 113

It is required to divide the line AB into two parts , so that the rectangle contained

by them may be equal to the square on M . M B A F с Bisect AB in C , with center

C , and radius CA or CB , describe the

...

It is required to divide the line AB into two parts , so that the rectangle contained

by them may be equal to the square on M . M B A F с Bisect AB in C , with center

C , and radius CA or CB , describe the

**semicircle**ADB . At the point B draw BE at...

Side 138

Let ABCD be a circle , and BAD , BED angles in the same segment BAED . Then

the angles BAD , BED shall be equal to one another . First , let the segment

BAED be greater than a

111 .

Let ABCD be a circle , and BAD , BED angles in the same segment BAED . Then

the angles BAD , BED shall be equal to one another . First , let the segment

BAED be greater than a

**semicircle**. A E Take F , the center of the circle ABCD , (111 .

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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.