## Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's and Playfair's Editions ... |

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Side 8

A circle is a plane figure enclosed by a uniformly curved line , called the

every point of the

centre to the ...

A circle is a plane figure enclosed by a uniformly curved line , called the

**circumference**. 14. The centre of a circle is a point within it , equidistant fromevery point of the

**circumference**. 15. A radius is any straight line drawn from thecentre to the ...

Side 127

Hence a polygon may be described about a circle , the perimeter of which shall

exceed the

Let No be the given line . Take in NO the part NP less than its half , and less than

...

Hence a polygon may be described about a circle , the perimeter of which shall

exceed the

**circumference**of the circle by a line that is less than any given line .Let No be the given line . Take in NO the part NP less than its half , and less than

...

Side 130

9 Th . The

less than ten of the parts of which the diameter contains seventy ; but greater than

ten of the parts of which the diameter contains seventy - one . Let C be the centre

...

9 Th . The

**circumference**of a circle exceeds three times its diameter , by a lineless than ten of the parts of which the diameter contains seventy ; but greater than

ten of the parts of which the diameter contains seventy - one . Let C be the centre

...

Side 131

Wherefore the

which the radius contains 1000 . The diameter , therefore , has to the

1000 has to ...

Wherefore the

**circumference**of a circle is less than 6285.461 of those parts ofwhich the radius contains 1000 . The diameter , therefore , has to the

**circumference**a less ratio ( p . 8 of b . 5 ) , than 2000 has to 6285.461 , or than1000 has to ...

Side 132

chord is the side of an inscribed polygon of 96 sides , the perimeter of which is 96

X65.4377 + = 6282.019 + : But the circumferenec of the circle exceeds the

perimeter of the inscribed polygon ; therefore the

6282.019+ ...

chord is the side of an inscribed polygon of 96 sides , the perimeter of which is 96

X65.4377 + = 6282.019 + : But the circumferenec of the circle exceeds the

perimeter of the inscribed polygon ; therefore the

**circumference**exceeds6282.019+ ...

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Euclid's Elements: Or, Second Lessons in Geometry,in the Order of Simson's ... Dennis M'Curdy Uten tilgangsbegrensning - 1846 |

Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Ingen forhåndsvisning tilgjengelig - 2017 |

Euclid's Elements, Or Second Lessons in Geometry, in the Order of Simson's ... D. M'Curdy Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

ABCD alternate antecedents applied Argument base bisected centre Chart chord circle circle ABC circumference common consequents Constr contained described diameter difference divided draw drawn equal angles equiangular equilateral equimultiples exceeds excess exterior extreme fore four fourth Geometry given given straight line gles greater half Hence inscribed interior join less magnitudes mean measure meet multiple namely opposite parallel parallelogram pass perpendicular plane polygon produced proportionals propositions proved Q. E. D. Recite radius ratio rectangle rectilineal figure remainders right angles School segment sides similar sine solid square straight line taken tangent third touch triangle ABC unequal Wherefore whole

### Populære avsnitt

Side 90 - If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals, the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

Side 117 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Side 92 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Side 79 - THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the sixth.

Side 87 - If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally...

Side 26 - Triangles upon equal bases, and between the same parallels, are equal to one another.

Side 133 - If a straight line stand at right angles to each of two straight lines at the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are.

Side 13 - AB be the greater, and from it cut (3. 1.) off DB equal to AC the less, and join DC ; therefore, because A in the triangles DBC, ACB, DB is equal to AC, and BC common to both, the two sides DB, BC are equal to the two AC, CB. each to each ; and the angle DBC is equal to the angle ACB; therefore the base DC is equal to the base AB, and the triangle DBC is< equal to the triangle (4. 1.) ACB, the less to 'the greater; which is absurd.

Side 71 - If the first magnitude be the same multiple of the second that the third is of the fourth, and the fifth the same multiple of the second that the sixth is of the fourth ; then shall...

Side 83 - IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to the last. NB This is usually cited by the words