## 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 |

### Inni boken

Resultat 1-5 av 99

Side 4

... except that of Euclid , has ever been

proportionals can be deduced by reasonings , which , at the same time that they

are perfectly rigorous , are also simple and direct . As to the defects , the

prolixness and ...

... except that of Euclid , has ever been

**given**; from which the properties ofproportionals can be deduced by reasonings , which , at the same time that they

are perfectly rigorous , are also simple and direct . As to the defects , the

prolixness and ...

Side 6

Solution of a problem is the resolution or answer

Numeral solution , is the answer

the answer

one ...

Solution of a problem is the resolution or answer

**given**to it . A Numerical orNumeral solution , is the answer

**given**in numbers . A Geometrical solution , isthe answer

**given**by the principles of Geometry . And a Mechanical solution , isone ...

Side 12

PROPOSITION I . PROBLEM . To describe an equilateral triangle upon a

finite straight line . Lot AB be the

equi . lateral triangle upon it . From the centre A , at the distance AB , describe ( 3

.

PROPOSITION I . PROBLEM . To describe an equilateral triangle upon a

**given**finite straight line . Lot AB be the

**given**straight line ; it is required to describe anequi . lateral triangle upon it . From the centre A , at the distance AB , describe ( 3

.

Side 13

Wherefore , from the

the

straight lines to cut off a part equal to the less . Let A B and C be the two

straight ...

Wherefore , from the

**given**point A , a straight line AL has been drawn equal tothe

**given**straight line BC . PROP . III . PROB . From the greater of two**given**straight lines to cut off a part equal to the less . Let A B and C be the two

**given**straight ...

Side 17

To bisect a

BAC be the

AB , and from AC cut ( 3 . 1 . ) off AE equal to AD ; join DE , and upon it describe ...

To bisect a

**given**rectilineal angle , that is , to divide it into two equal angles . LetBAC be the

**given**rectilineal angle , it is required to bisect it . Take any point D inAB , and from AC cut ( 3 . 1 . ) off AE equal to AD ; join DE , and upon it describe ...

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1840 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1845 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1852 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 51 - 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 12 - AB; but things which are equal to the same are equal to one another...

Side 80 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.

Side 288 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 35 - Parallelograms upon the same base and between the same parallels, are equal to one another.

Side 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by this line with the line which touches the circle, shall be equal to the angles in the alternate segments of the circle.

Side 52 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Side 127 - 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 23 - If, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than, the other two sides of the triangle, but shall contain a greater angle.

Side 19 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it the angles CBA, ABD ; these are either two right angles, or are together equal to two right angles. For, if the angle CBA be equal to ABD, each of them is a right angle (Def.