## 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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Side 42

All the interior angles of any rectilineal figure are equal to twice as many right

angles as the figure has sides , wanting

figure ABCDE can be divided into as many triangles as the figure has sides , by

drawing ...

All the interior angles of any rectilineal figure are equal to twice as many right

angles as the figure has sides , wanting

**four**right angles . For any rectilinealfigure ABCDE can be divided into as many triangles as the figure has sides , by

drawing ...

Side 110

If

said to be triplicate of the ratio of the first to the second , or of the ratio of the

second to the third , & c . " So also , if there are five continual proportionals ; the

ratio ...

If

**four**magnitudes are continual proportionals , the ratio of the first to the fourth issaid to be triplicate of the ratio of the first to the second , or of the ratio of the

second to the third , & c . " So also , if there are five continual proportionals ; the

ratio ...

Side 137

If

equal to the rectangle contained by the ... Let the

F be proportionals , viz . as AB to CD , so E to F ; the rectangle contained by AB ...

If

**four**straight lines be proportionals , the rectangle contained by the extremes isequal to the rectangle contained by the ... Let the

**four**straight lines , AB , CD , E ,F be proportionals , viz . as AB to CD , so E to F ; the rectangle contained by AB ...

Side 222

and therefore also , the angle ABC is to

AC to

and therefore also , the angle ABC is to

**four**times the anE gle ABD as the archAC to

**four**times K B the arch AD ( 4. 5. ) ; But ABD is a right angle , and therefore**four**times the arch AD is equal to the whole circumference ACF ; therefore , the ... Side 308

Then , because the line CD has turned about one of its extremities till it has come

G into the position CD again , it has by the corollary to the above definition

described angles which are together equal to

which ...

Then , because the line CD has turned about one of its extremities till it has come

G into the position CD again , it has by the corollary to the above definition

described angles which are together equal to

**four**right angles ; but the angleswhich ...

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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1824 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common contained cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior 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 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.