## 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

If between the

Index of this will be for its Distance from Unity will be one half of the Distance of a

from Unity ; and fo a { may be written ✓ a . And if a mean proportional be put ...

If between the

**Terms**i and a , there be put a mean Proportional which is d , theIndex of this will be for its Distance from Unity will be one half of the Distance of a

from Unity ; and fo a { may be written ✓ a . And if a mean proportional be put ...

Side 329

Likewise in this new Series , the Right Lines A L , AC , express the Diftances of

the

shall be the tenth

Likewise in this new Series , the Right Lines A L , AC , express the Diftances of

the

**Terms**L M , CD , from Unity , viz . Since AL is ten times greater than Ac , L Mshall be the tenth

**Term**of the Series from Unity : And because Ae is three times ... Side 330

Now in this new Series , the Distances AL , AC , & c . will determine the Orders or

Places of the

fourth

Unity .

Now in this new Series , the Distances AL , AC , & c . will determine the Orders or

Places of the

**Terms**; viz . if AL be five times greater than A C , and CD be thefourth

**Term**of the Series from Unity , then LM will be the twentieth**Term**frontUnity .

Side 365

10000 113 : 32 EXAMPLE Let it be required to find a Rank of Ratios , whose

to 31416 , which expresles nearly , the Proportion of the Diameter of the Circle ,

to ...

10000 113 : 32 EXAMPLE Let it be required to find a Rank of Ratios , whose

**Terms**are integral ; and the nearest pofsible to the following Ratio , viz . of 10000to 31416 , which expresles nearly , the Proportion of the Diameter of the Circle ,

to ...

Side 370

And to find the Logarithm of the Ratio of any two

greater , it will be as a : b :: b 1 : 1 ** : * ' ; or the Difference divided by the lesser

...

And to find the Logarithm of the Ratio of any two

**Terms**, a the least and b thegreater , it will be as a : b :: b 1 : 1 ** : * ' ; or the Difference divided by the lesser

**Term**when ' tis an increasing Ratio , and bra when ' tis decreasing . b Wherefore...

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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.