## 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

Side 11

... one of them is greater than the other : Let AB be the greater , and from it cut off

DB equal to AC the less , and

D ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are ...

... one of them is greater than the other : Let AB be the greater , and from it cut off

DB equal to AC the less , and

**join**DC ; therefore , because in the triangles DBC ,D ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are ...

Side 14

EF equal to BE ;

and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle E AEB

...

**Join**B and E the middle point of the line AC , and produce BE to F , А. and makeEF equal to BE ;

**join**also FC , and produce AC to G. Because AE is equal to EC ,and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle E AEB

...

Side 15

A AB ; the angle ABC is also greater than the angle BCA . Make AD equal to AB ,

and

greater ( 9. 1. ) D than the interior and opposite angle DCB ; but ADB is equal ( 3.

1. ) ...

A AB ; the angle ABC is also greater than the angle BCA . Make AD equal to AB ,

and

**join**BD : and because ADB is the exterior angle of the triangle BDC , it isgreater ( 9. 1. ) D than the interior and opposite angle DCB ; but ADB is equal ( 3.

1. ) ...

Side 17

EDG equal to the angle BAC : and make DG equal to AC or DF , and

Because AB is equal А D to DE , and AC to DG , the two sides BA , AC are equal

to the two ED , DG , each to each , and the angle BAC is equal to the angle EDG

...

EDG equal to the angle BAC : and make DG equal to AC or DF , and

**join**EG , GFBecause AB is equal А D to DE , and AC to DG , the two sides BA , AC are equal

to the two ED , DG , each to each , and the angle BAC is equal to the angle EDG

...

Side 18

Their equality would be manifest , if the third sides BC and EF were equal . If

possible , suppose that those sides are not equal , and that BC is the greater .

Take BH = EF ; and

E are ...

Their equality would be manifest , if the third sides BC and EF were equal . If

possible , suppose that those sides are not equal , and that BC is the greater .

Take BH = EF ; and

**join**AH . The triangle ABH = DEF ; for the right angles B andE are ...

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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 - 1854 |

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

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC base bisected Book called centre chord circle circumference coincide common consequently construction cosine cylinder definition demonstrated described diameter difference distance divided double draw drawn equal equal angles equiangular equilateral Euclid exterior angle extremities 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