## 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 63

Side 45

It must , however , be carefully remarked , that the third postulate only admits that

when any line is given in position and magnitude , a circle may be described from

either extremity of the line as a center , and with a

It must , however , be carefully remarked , that the third postulate only admits that

when any line is given in position and magnitude , a circle may be described from

either extremity of the line as a center , and with a

**radius**equal to the length of ... Side 51

The construction of this problem assumes a neater form , by first describing the

circle CGH with center B and

equilateral triangle DBA to meet the circumference in G : next , with center D and

The construction of this problem assumes a neater form , by first describing the

circle CGH with center B and

**radius**BC , and producing DB the side of theequilateral triangle DBA to meet the circumference in G : next , with center D and

**radius**... Side 53

The third postulate requires that the line CD should be drawn before the circle

can be described with the center C , and

Prop . XIII . “ Upon the opposite sides of it . " " If these words were omitted , it is ...

The third postulate requires that the line CD should be drawn before the circle

can be described with the center C , and

**radius**CD . Prop . xlv . is the converse ofProp . XIII . “ Upon the opposite sides of it . " " If these words were omitted , it is ...

Side 60

A circle may be described from any center , with any straight line as

How does this postulate differ from Euclid ' s , and which of his problems is

assumed in it ? 17 . What principles in the Physical Sciences correspond to

axioms in ...

A circle may be described from any center , with any straight line as

**radius**. "How does this postulate differ from Euclid ' s , and which of his problems is

assumed in it ? 17 . What principles in the Physical Sciences correspond to

axioms in ...

Side 61

tances DG , DH may be taken as the

proof in each case . 36 . Explain how the propositions Euc . 1 . 2 , 3 , are

rendered necessary by the restriction imposed by the third postulate . Is it

necessary for the ...

tances DG , DH may be taken as the

**radius**of the second circle ; and give theproof in each case . 36 . Explain how the propositions Euc . 1 . 2 , 3 , are

rendered necessary by the restriction imposed by the third postulate . Is it

necessary for the ...

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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.