## 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 11

To draw a

the same . ET A B be the given

draw a

...

To draw a

**Right Line**at Right Angles to a given**Right Line**, from a given Point inthe same . ET A B be the given

**Right Line**, and the given Point . It is required todraw a

**Right Line**from the Point C , at Right Angles to A B. Afsume any Point D in...

Side 13

Wherefore when a

, these shall be either two Right Angles , or ... THEORE M. 1 If to any

and Point therein , two

Wherefore when a

**Right Line**, standing upon another**Right Line**, makes Angles, these shall be either two Right Angles , or ... THEORE M. 1 If to any

**Right Line**,and Point therein , two

**Right Lines**be drawn from contrary Parts , making the ... Side 29

themselves . N ET AB and CD be

upon ...

**Right Lines**parallel to one and the same**Right Line**, are also parallel betweenthemselves . N ET AB and CD be

**Right Lines**, each of which is parallel to the**Right Line**EF . I say A B is also parallel to CD . For let the**Right Line**. GK fallupon ...

Side 66

THEOREM . if in a Circle a

Angles ; and if it cuts it at Right Angles , it all cut it into two equal Parts . ET ABC

be a ...

THEOREM . if in a Circle a

**Right Line**drawn thro ' the Center , cuts any other**Right Line**not drawn throm the Center , into equal Parts , it fall cut it at RightAngles ; and if it cuts it at Right Angles , it all cut it into two equal Parts . ET ABC

be a ...

Side 92

I say , moreover , the Angle of the greater Segment contained under the

Circumference ABC , and the

because the Angle contained under the

the Angle ...

I say , moreover , the Angle of the greater Segment contained under the

Circumference ABC , and the

**Right Line**AC , is ... This manifestly appears ; forbecause the Angle contained under the

**Right Lines**BA , AC , is a Right Angle ,the Angle ...

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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.