## 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 328

put a mean Proportional which is d , the Index of this will be for its

Unity will be one half of the

**Distance**that every Term is from Unity . ... If between the Terms i and a , there beput a mean Proportional which is d , the Index of this will be for its

**Distance**fromUnity will be one half of the

**Distance**of a from Unity ; and fo a { may be written ... Side 332

The

those Numbers , and indeed doth not measure the Ratio itself , but the Number of

Terms in a given Series of Geometrical Proportionals proceeding from one ...

The

**Distance**between any two Numbers , is called the Logarithm of the Ratio ofthose Numbers , and indeed doth not measure the Ratio itself , but the Number of

Terms in a given Series of Geometrical Proportionals proceeding from one ...

Side 334

For Example , if un be the firft Term of the Series from Unity A B , the Logarithm

thereof , or the

Increment of the Number above Unity , As suppose un be 1,0000001 , he placed

0 ...

For Example , if un be the firft Term of the Series from Unity A B , the Logarithm

thereof , or the

**Distance**An , or By , was , according to him , equal to vy , or theIncrement of the Number above Unity , As suppose un be 1,0000001 , he placed

0 ...

Side 336

0 , 6748. o , 06748 , are continual Proportionals in the Ratio of 10 to 1 ; and so

their

8291751

...

0 , 6748. o , 06748 , are continual Proportionals in the Ratio of 10 to 1 ; and so

their

**Distances**from each 6 7 4 8 3,8291751 other shall be equal to the 67 4,8 2,8291751

**Distance**or Logarithm of 6 7 , 48 1,8291751 the Number 10 , or equal 6...

Side 338

tinual Proportionals , their

another . And to it is manifeft ; that the

double of the

is triple of ...

tinual Proportionals , their

**Distances**from each other shall be equal to oneanother . And to it is manifeft ; that the

**Distance**of the Square from Unity , isdouble of the

**Distance**of its Root from the fame : Also the Diftance of the Cube ,is triple of ...

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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.