## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 6

Side 71

2 straight lines FB , FC , FG , & c . that can be

FA is the greatest , and FD , the other part of the diameter AD , is the least : and of

the others , FB is greater than FC , and FC than FG . Join BE , CE , GE ; and ...

2 straight lines FB , FC , FG , & c . that can be

**drawn**from F to the circumference ,FA is the greatest , and FD , the other part of the diameter AD , is the least : and of

the others , FB is greater than FC , and FC than FG . Join BE , CE , GE ; and ...

Side 77

The straight line

extremity of it , falls without the circle ; and no straight line can be

that straight line and the circumference , from ihe extremity of the diameter , so as

not to ...

The straight line

**drawn**at right angles to the diameter of a circle , from theextremity of it , falls without the circle ; and no straight line can be

**drawn**betweenthat straight line and the circumference , from ihe extremity of the diameter , so as

not to ...

Side 78

from D

angle , and the angle DAH less than a ... From this it is manifest , that the straight

line which is

it ...

from D

**draw**DH at right angles to AG ; and because the angle DHA is a right Gangle , and the angle DAH less than a ... From this it is manifest , that the straight

line which is

**drawn**at right angles to the diameter of a circie from the extremity ofit ...

Side 79

If a straight line touch a circle , the straight line

of contact , is perpendicular to the line touching the circle . Let the straight line DE

touch the circle ABC in the point C ; take the centre F , and

If a straight line touch a circle , the straight line

**drawn**from the centre to the pointof contact , is perpendicular to the line touching the circle . Let the straight line DE

touch the circle ABC in the point C ; take the centre F , and

**draw**the straight line ... Side 155

... straight lines be

lines

point of bisection , the same ratio which the straight line subtending the arch has

to ...

... straight lines be

**drawn**to any point in the circumference , the sum of the twolines

**drawn**from the extremities of the arch will have to the line**drawn**from thepoint of bisection , the same ratio which the straight line subtending the arch has

to ...

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Elements of Geometry: Containing the First Six Books of Euc, With a ... Formerly Chairman Department of Immunology John Playfair,John Playfair Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced PROP proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole

### Populære avsnitt

Side 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.

Side 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Side 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...

Side 130 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...

Side 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Side 55 - 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.