## 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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Resultat 1-5 av 33

Side 13

... greater than either of the

and let its side BC be produced to D , the exteF rior angle ACD is greater than

either of the

... greater than either of the

**interior**, and opposite angles . Lot ABC be a triangle ,and let its side BC be produced to D , the exteF rior angle ACD is greater than

either of the

**interior**OF GEOMETRY . 13 BOOK I. Side 14

F rior angle ACD is greater than either of the

Join B and E the middle point of the line AC , and produce BE to F , А. and make

EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC ...

F rior angle ACD is greater than either of the

**interior**opposite angles CBA , BAC .Join B and E the middle point of the line AC , and produce BE to F , А. and make

EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC ...

Side 15

D than the

because the side AB is equal to the side . B AD ; therefore the angle ABD is

likewise greater than the angle ACB ; wherefore much more is the angle ABC

greater ...

D than the

**interior**and opposite angle DCB ; but ADB is equal ( 3. 1. ) to ABD ,because the side AB is equal to the side . B AD ; therefore the angle ABD is

likewise greater than the angle ACB ; wherefore much more is the angle ABC

greater ...

Side 16

is greater than the

triangle CDE is greater than CED ; for the same reason , the exterior angle CEB

of the triangle ABE is greater than BAC ; and it has been demonstrated that the

angle ...

is greater than the

**interior**and opposite angle , the exterior angle BDC of thetriangle CDE is greater than CED ; for the same reason , the exterior angle CEB

of the triangle ABE is greater than BAC ; and it has been demonstrated that the

angle ...

Side 19

than the

impossible : therefore , AB and CD being produced , do not meet towards B , D. In

like manner it may be demonstrated that they do not meet towards A , C ; but

those ...

than the

**interior**and opposite angle EFG ; but it is also equal to it , which isimpossible : therefore , AB and CD being produced , do not meet towards B , D. In

like manner it may be demonstrated that they do not meet towards A , C ; but

those ...

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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 - 1824 |

### 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 square straight line taken tangent THEOR third touch triangle ABC wherefore whole