## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |

### Inni boken

Resultat 1-5 av 33

Side 29

IF a straight line

equal to one another , these two straight lines are parallel . Let the straight line

EF , which

AEF ...

IF a straight line

**falling**upon two other straight lines make the alternate anglesequal to one another , these two straight lines are parallel . Let the straight line

EF , which

**falls**upon the two straight lines AB , CD , make the alternate anglesAEF ...

Side 30

11 IF a straight line

equal to the interior and opposite upon the same side of the line , or make the

interior angles upon the same side together equal to two right angles ; the two ...

11 IF a straight line

**falling**upon two other straight lines make the exterior angleequal to the interior and opposite upon the same side of the line , or make the

interior angles upon the same side together equal to two right angles ; the two ...

Side 31

Let the straight line EF

alternate angles AGH , GHD are equal to one another ; and the exterior angle

EGB is equal to the interior and opposite angle GHD , upon the same side ; and

the ...

Let the straight line EF

**fall**upon the parallel straight lines Book I. AB , CD ; thealternate angles AGH , GHD are equal to one another ; and the exterior angle

EGB is equal to the interior and opposite angle GHD , upon the same side ; and

the ...

Side 33

... meets them , the alternate angles BAC , B C ACE are equalb . Again , because

AB is parallel to CE , and b 29. 1 . BD

equal to the interior and opposite angle ABC ; but the angle ACE was shown to ...

... meets them , the alternate angles BAC , B C ACE are equalb . Again , because

AB is parallel to CE , and b 29. 1 . BD

**falls**upon them , the exterior angle ECD isequal to the interior and opposite angle ABC ; but the angle ACE was shown to ...

Side 43

Then because the straight line HF

AHF , HFE are together equal to two c 29. 1 . right angles ; wherefore the angles

BHF , HFE are less than two right angles ; therefore HB , FE will meetd , if

produced ...

Then because the straight line HF

**falls**upon the parallels AH , EF , the anglesAHF , HFE are together equal to two c 29. 1 . right angles ; wherefore the angles

BHF , HFE are less than two right angles ; therefore HB , FE will meetd , if

produced ...

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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 - 1847 |

### Vanlige uttrykk og setninger

ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch base bisected Book centre circle circle ABC circumference coincide common compounded contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples exterior angle extremities fall figure fore fourth given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced proportional proposition proved pyramid Q. E. D. PROP ratio reason rectangle contained rectilineal figure right angles segment shown sides similar solid space square taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 121 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.

Side 3 - 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 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.

Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Side 291 - 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 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...

Side 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.

Side 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.