## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ... |

### Inni boken

Resultat 1-5 av 26

Side 31

to the angle CEF , because they are vertical angles ; there B D

is equal ( 4. 1. ) to the base CF , and the triangle AEB to the triangle CEF , and .

the remaining angles to the remaining angles , each to each , to G which the

equal ...

to the angle CEF , because they are vertical angles ; there B D

**fore**the base ABis equal ( 4. 1. ) to the base CF , and the triangle AEB to the triangle CEF , and .

the remaining angles to the remaining angles , each to each , to G which the

equal ...

Side 39

to two right angles , the angles AGH , BGH are equal to the angles BGH , GHD :

Take away the common angle BGH ; therefore the remaining angle AGH is equal

to the remaining angle GHD ; and they are alternate angles ; there .

to two right angles , the angles AGH , BGH are equal to the angles BGH , GHD :

Take away the common angle BGH ; therefore the remaining angle AGH is equal

to the remaining angle GHD ; and they are alternate angles ; there .

**fore**AB is ... Side 42

to two right angles ; therefore all the interior , together with all the exterior angles

of the figure , are equal to twice as many right angles as there are sides of the fic

gure ; that is , by the

to two right angles ; therefore all the interior , together with all the exterior angles

of the figure , are equal to twice as many right angles as there are sides of the fic

gure ; that is , by the

**fore**D B going corollary , they are equal to all the interior ... Side 47

B

c . Q. E. D. PROP . XLII . PROB . To describe a parallelogram that shall be equal

to a given triangle , and have one of its angles equal to a given rectilineal angle .

B

**fore**ABCD is also double of the triangle EBC . Therefore , if a parallelogram , &c . Q. E. D. PROP . XLII . PROB . To describe a parallelogram that shall be equal

to a given triangle , and have one of its angles equal to a given rectilineal angle .

Side 57

the square ADEB , and construct the figure as in the preceding propositions :

Because AG = GE , AG + CK = GE + CK , that is , AK = CE , and thereА.

CE = 2AK . But AK + CE = c B. gnomon AKF + CK ; and therefore , AKF + CK =

2AK ...

the square ADEB , and construct the figure as in the preceding propositions :

Because AG = GE , AG + CK = GE + CK , that is , AK = CE , and thereА.

**fore**AK +CE = 2AK . But AK + CE = c B. gnomon AKF + CK ; and therefore , AKF + CK =

2AK ...

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1836 |

Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Uten tilgangsbegrensning - 1837 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |

### 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 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 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 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...

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 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 308 - 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 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 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.

Side 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Side 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.