## Euclid's Elements of Geometry: From the Latin Translation of Commandine. To which is Added, A Treatise of the Nature of Arithmetic of Logarithms ; Likewise Another of the Elements of Plain and Spherical Trigonometry ; with a Preface |

### Inni boken

Resultat 1-5 av 5

Side 63

A Right Line is said to

produced , does not cut it . II . Circles are said to

distant from ...

A Right Line is said to

**touch**a Circle when**touching**the same , and beingproduced , does not cut it . II . Circles are said to

**touch**each other , which**Touching**do not cut one another . V. Right Lines in a Circle are said to be equallydistant from ...

Side 76

THE O R E M. One Circle cannot

it be inwardly , or outwardly . FORMA OR , in the first place , if this be denied , let

the Circle ABDC , if possible ,

THE O R E M. One Circle cannot

**touch**another in more Points than one , whetherit be inwardly , or outwardly . FORMA OR , in the first place , if this be denied , let

the Circle ABDC , if possible ,

**touch**the Circle EBFD inwardly , in more Points ... Side 98

And because DE

AD , and DC , will be equal to the Square of DE . But the Rectangle un1 By Hyp .

der AD and DC , is equal to the Square of DB . Wherefore the Square of D E ...

And because DE

**touches**the Circle ABC , and DCA cuts it , the Rectangle underAD , and DC , will be equal to the Square of DE . But the Rectangle un1 By Hyp .

der AD and DC , is equal to the Square of DB . Wherefore the Square of D E ...

Side 203

PROPOSITION XV , THEOREM , If two Right Lines ,

parallel to two Right Lines ,

are in the fame Plane ; but GH and GK , which are both in the fame Plane ,

it .

PROPOSITION XV , THEOREM , If two Right Lines ,

**touching**one another , beparallel to two Right Lines ,

**touching**... 3 . with all Right Lines that**touch**it , andare in the fame Plane ; but GH and GK , which are both in the fame Plane ,

**touch**it .

Side 268

And since LN is parallel to AC , and AC

therein of equal Sides , even in Number , that does not

. which ...

And since LN is parallel to AC , and AC

**touches**the Circle EFGH , LN will not**touch**the Circle EFGH . ... Circle ABCD , we shall have a Polygon inscribedtherein of equal Sides , even in Number , that does not

**touch**the leffer Circle EFG. which ...

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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ... John Keill Uten tilgangsbegrensning - 1723 |

### Vanlige uttrykk og setninger

added alſo Altitude Angle ABC Baſe becauſe Center Circle Circle ABCD Circumference common Cone conſequently contained Cylinder demonſtrated deſcribed Diameter Difference Diſtance divided double draw drawn equal equal Angles equiangular Equimultiples exceeds fall fame firſt fore four fourth given greater half join leſs likewiſe Logarithm Magnitudes Manner mean Multiple Number oppoſite parallel Parallelogram perpendicular Place Plane Point Polygon Priſms produced Prop Proportion PROPOSITION proved Pyramid Radius Ratio Rectangle remaining Right Angles Right Line Right-lined Figure ſaid ſame ſame Reaſon ſay ſecond Segment Series ſhall ſhall be equal Sides ſimilar ſince Sine Solid ſome Sphere Square ſtand taken Terms THEOREM thereof theſe third thoſe thro touch Triangle Triangle ABC Unity Wherefore whole whoſe Baſe

### Populære avsnitt

Side 66 - 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.

Side 161 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.

Side 110 - And in like manner it may be shown that each of the angles KHG, HGM, GML is equal to the angle HKL or KLM ; therefore the five angles GHK, HKL, KLM, LMG, MGH...

Side 88 - IN a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Side 22 - ... sides equal to them of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB...

Side 9 - ... equal to them, of the other. Let ABC, DEF be two triangles which have the two sides AB, AC equal to the two sides DE, DF, each to each, viz. AB equal to DE, and AC to DF ; but the base CB greater than the base EF ; the angle BAC is likewise greater than the angle EDF.

Side 15 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...

Side 33 - ... therefore their other sides are equal, each to each, and the third angle of the one to the third angle of the other, (i.

Side 111 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.