## 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 6-10 av 74

Side 48

It may be observed that when equal magnitudes are

magnitudes , the greater remainder exceeds the less remainder by as much as

the greater of the unequal magnitudes exceeds the less . If unequals be

from ...

It may be observed that when equal magnitudes are

**taken**from unequalmagnitudes , the greater remainder exceeds the less remainder by as much as

the greater of the unequal magnitudes exceeds the less . If unequals be

**taken**from ...

Side 51

The term base is obviously

be said of the term altitude . In Geometry , however , these terms are not restricted

to one particular position of a figure , as in the case of a building , but may be in ...

The term base is obviously

**taken**from the idea of a building , and the same maybe said of the term altitude . In Geometry , however , these terms are not restricted

to one particular position of a figure , as in the case of a building , but may be in ...

Side 54

... if one circle lies partly within and partly without another circle , the

circumferences of the circles intersect each other in two points . Prop . XXIII . CD

might be

isosceles triangle .

... if one circle lies partly within and partly without another circle , the

circumferences of the circles intersect each other in two points . Prop . XXIII . CD

might be

**taken**equal to CE , and the construction effected by means of anisosceles triangle .

Side 56

is

sense in which Euclid applies the third axiom , is to be retained here . It may be

observed , that the two parallelograms exhibited 56 EUCLID ' S ELEMENTS .

is

**taken**twice from the trapezium , which would appear to be impossible , if thesense in which Euclid applies the third axiom , is to be retained here . It may be

observed , that the two parallelograms exhibited 56 EUCLID ' S ELEMENTS .

Side 60

2 , if DB a side of the equilateral triangle DAB be produced both ways and cut the

circle whose center is B and radius BC in two points G and H ; shew that either of

the dis . tances DG , DH may be

2 , if DB a side of the equilateral triangle DAB be produced both ways and cut the

circle whose center is B and radius BC in two points G and H ; shew that either of

the dis . tances DG , DH may be

**taken**as the radius 60 EUCLID ' S ELEMENTS ...### 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.