## 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 23

Side 4

The extremities of a line are points ; and the intersections “ of one line with

another are also points . ” 3. “ If two lines are such that they cannot

any two points , with“ out coinciding altogether , each of them is called a straight

line .

The extremities of a line are points ; and the intersections “ of one line with

another are also points . ” 3. “ If two lines are such that they cannot

**coincide**inany two points , with“ out coinciding altogether , each of them is called a straight

line .

Side 7

The denomination , equal figures , we shall reserve for such as , when applied to

each other ,

equal radii ; two triangles , which have all their sides equal respectively , & c .

The denomination , equal figures , we shall reserve for such as , when applied to

each other ,

**coincide**in all their points : of this kind are two circles , which haveequal radii ; two triangles , which have all their sides equal respectively , & c .

Side 8

7. Things which are halves of the same thing , are equal to one another . 8. Two

magnitudes , lines , surfaces , or solids , are equal , if , when applied to each

other , they

. 9.

7. Things which are halves of the same thing , are equal to one another . 8. Two

magnitudes , lines , surfaces , or solids , are equal , if , when applied to each

other , they

**coincide**throughout their whole extent . They then fill the same space. 9.

Side 9

Therefore also the whole triangle ABC shall

, so that the spaces which they contain or their areas are equal ; and the

remaining angles of the one shall

, and ...

Therefore also the whole triangle ABC shall

**coincide**with the whole triangle DEF, so that the spaces which they contain or their areas are equal ; and the

remaining angles of the one shall

**coincide**with the remaining angles of the other, and ...

Side 65

... and D common to both arcs ; the two extremities , therefore , of the arc AFD ,

thus coinciding with those of the arc A B BGD , all the intermediate parts must

Conversely .

... and D common to both arcs ; the two extremities , therefore , of the arc AFD ,

thus coinciding with those of the arc A B BGD , all the intermediate parts must

**coincide**, inasmuch as they are all equally disF G D tant from the centre .Conversely .

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

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1847 |

### 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