## 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 6

Side 285

I. 1.2 a z3 a zs 2 , b a z4 I 1.2 are the Terms of the

Sine in Numbers true to a given Place of Figures . And then when the Arc is

nearly equal to the Radius , the

remedy ...

I. 1.2 a z3 a zs 2 , b a z4 I 1.2 are the Terms of the

**Series**required to have theSine in Numbers true to a given Place of Figures . And then when the Arc is

nearly equal to the Radius , the

**Séries**converges very pow . And therefore , toremedy ...

Side 286

In the first and fecond

become Radius , or i . And hence , if the Terms wherein a is , are taken away ,

and i to be put instead of b , the

and ...

In the first and fecond

**Series**, if A = 0 ; then shall a = o , and b its Cofre , willbecome Radius , or i . And hence , if the Terms wherein a is , are taken away ,

and i to be put instead of b , the

**Series**will become the Newtonian . In the thirdand ...

Side 329

The Lines A C , AE , AG , AI , AL - A , - AI , respectively express the Distances of

the Numbers from Unity , or the Place and Order that every Number obtains in the

The Lines A C , AE , AG , AI , AL - A , - AI , respectively express the Distances of

the Numbers from Unity , or the Place and Order that every Number obtains in the

**Series**of Geometrical Proportionals , according as it is distant from Unity . Side 330

If , again the Distances Ac , cC , Cè , e E , & c . be supposed to be bisected , and

mean Proportionals , between every two of the Terms , be conceived to be put at

those middle Distances ; then there will arise another

If , again the Distances Ac , cC , Cè , e E , & c . be supposed to be bisected , and

mean Proportionals , between every two of the Terms , be conceived to be put at

those middle Distances ; then there will arise another

**Series**of Proportionals ... Side 354

1 I 1 + Numbers to any Number of Places may be had more expediently and truer

: Concerning which

Philofophical Transactions , wherein he has demonstrated those

new Way ...

1 I 1 + Numbers to any Number of Places may be had more expediently and truer

: Concerning which

**Series**Dr. Halley has written a learned Tract , in thePhilofophical Transactions , wherein he has demonstrated those

**Series**after anew Way ...

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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.