## 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 |

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Side 33

The opposite Sides and opposite Angles of any Parallelogram are equal ; and

the

Parallelogram , whose

Angles are ...

The opposite Sides and opposite Angles of any Parallelogram are equal ; and

the

**Diameter**divides ibe same into two equal Parts . ET ABDC be aParallelogram , whose

**Diameter**is BC . I say , the opposite Sides and oppositeAngles are ...

Side 39

In every Parallelogram the Complements of the Parallelograms that stand about

the

, whose

In every Parallelogram the Complements of the Parallelograms that stand about

the

**Diameter**, are equal between themselves . LEI ET ABCD be a Parallelogram, whose

**Diameter**iş DB ; and let FH , EĞ , be Parallelograms standing about the ... Side 79

fore B C is greater than F G. And so the

greater than F G. Wherefore the

all the other Lines therein , that which is nearest to the Center is greater than that

...

fore B C is greater than F G. And so the

**Diameter**AD is the greatest , and B C isgreater than F G. Wherefore the

**Diameter**is the greatest Line in a Circle ; and ofall the other Lines therein , that which is nearest to the Center is greater than that

...

Side 178

I say the Parallelogram ABCD is about the same

AF . For if it be not , let AHC be the

be produced to H ; also let HK be drawn parallel to AD , or BC . Then because ...

I say the Parallelogram ABCD is about the same

**Diameter**with the ParallelogramAF . For if it be not , let AHC be the

**Diameter**of the Parallelogram BD , and let GFbe produced to H ; also let HK be drawn parallel to AD , or BC . Then because ...

Side 269

14circle about the

Semicircle is conceived to be , the Plane in which it is shall make a Circle in the

Superficies of the Sphere . It is also manifest that this Circle is a great Circle ,

since ...

14circle about the

**Diameter**which is at rest : In what- 11 . soever Position theSemicircle is conceived to be , the Plane in which it is shall make a Circle in the

Superficies of the Sphere . It is also manifest that this Circle is a great Circle ,

since ...

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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.