## 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 21

the angle ACD , is greater than the angle ABC . B D PROP . XVII . THEOR . Any

two angles of a triangle are together less than two

triangle ; any A two of its angles together are less than two

...

the angle ACD , is greater than the angle ABC . B D PROP . XVII . THEOR . Any

two angles of a triangle are together less than two

**right angles**. Let ABC be anytriangle ; any A two of its angles together are less than two

**right angles**. Produce...

Side 27

THEOR . , If a straight line falling upon two other straight lines makes the exterior

angle equal to the interior and opposite upon the same side of the line ; or makes

the interior angles upon the same side together equal to two

THEOR . , If a straight line falling upon two other straight lines makes the exterior

angle equal to the interior and opposite upon the same side of the line ; or makes

the interior angles upon the same side together equal to two

**right angles**; the ... Side 28

angle AGH , the angle AGH is equal to the angle GHD ; and they are th . alternate

angles ; therefore AB is parallel ( 27. 1. ) to CD . Again , because the angles BGH

, GHD are equal ( hyp . ) to two

angle AGH , the angle AGH is equal to the angle GHD ; and they are th . alternate

angles ; therefore AB is parallel ( 27. 1. ) to CD . Again , because the angles BGH

, GHD are equal ( hyp . ) to two

**right angles**, and AGH , BGH , are also equal ... Side 29

two

line perpendicular to one of two parallels , is perpendicular to the other . Cor . 3.

two

**right angles**; therefore the other two , HGL , GHD are greater than two**right****angles**. ... If BGH is a**right angle**, GHD will be a**right angle**also ; therefore everyline perpendicular to one of two parallels , is perpendicular to the other . Cor . 3.

Side 30

XXXII . THEOR . If a side of any triangle be produced , the exterior angle is equal

to the two interior and opposite angles ; and the three interior angles of every

triangle are equal to two

sides ...

XXXII . THEOR . If a side of any triangle be produced , the exterior angle is equal

to the two interior and opposite angles ; and the three interior angles of every

triangle are equal to two

**right angles**. Let ABC be a triangle , and let one of itssides ...

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Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1853 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1839 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circle ABC circumference coincide common consequently construction 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 right angles segment shewn sides similar sine solid spherical square straight line taken tangent THEOR third touch triangle ABC wherefore whole

### Populære avsnitt

Side 53 - 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 18 - If two triangles have two sides of the one equal to two sides of the...

Side 54 - 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 on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

Side 82 - 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 31 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.

Side 11 - 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 21 - 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 shall either be two right angles, or shall together be equal to two right angles. For...

Side 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Side 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.

Side 298 - 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.