## 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

Side 52

If a Right Line be any bow cui , the Square of the whole Line , together with the

Square of one of the Segments , is equal to

under the whole Line , and the said Segment , together with the Square , made of

the ...

If a Right Line be any bow cui , the Square of the whole Line , together with the

Square of one of the Segments , is equal to

**double**the Rectangle containedunder the whole Line , and the said Segment , together with the Square , made of

the ...

Side 56

Therefore the Square of E A is

is equal to GF , and the Square of E G is equal to the Square of GF : Therefore the

Squares of EG , GF , together , are

Therefore the Square of E A is

**double**to the Square of AC . Again , because EGis equal to GF , and the Square of E G is equal to the Square of GF : Therefore the

Squares of EG , GF , together , are

**double**to the Square of GF . But the Square ... Side 83

THEOREM . the Angle at the Center of a Circle is

Circumference , when the same Arc is the Base of the Angles . ET ABC be a

Circle , at the Center whereof L is the Angle BEC , and at the Circumference the

Angle ...

THEOREM . the Angle at the Center of a Circle is

**double**to the Angle at theCircumference , when the same Arc is the Base of the Angles . ET ABC be a

Circle , at the Center whereof L is the Angle BEC , and at the Circumference the

Angle ...

Side 111

Therefore the Angle BFC is

to the Angle FKC : For the same Reason , the Angle CFD is

CFL , and the Angle CLD

Therefore the Angle BFC is

**double**to the Angle KFC , and the Angle BKC**double**to the Angle FKC : For the same Reason , the Angle CFD is

**double**to the AngleCFL , and the Angle CLD

**double**to the Angle CLF : " And because the Cir ... Side 112

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

John Keill Mr. Cunn (Samuel), John Ham. HK is

BK ...

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

John Keill Mr. Cunn (Samuel), John Ham. HK is

**double**to BK . Again , becauseBK ...

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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.