## 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 16

For produce B C to D. Then because the outward Angle ACD of the * 16 of tbis .

...

For produce B C to D. Then because the outward Angle ACD of the * 16 of tbis .

**Triangle ABC**, is greater * than the inward opposite**Angle ABC**: If the common**Angle ACB**be added , the Angles A CD , ACB , together , will be greater than the...

Side 91

I say , the Angle which is in the Semicircle BAC is a Right Angle , that which is in

the Segment ABC being greater than a Semicircle , viz . the

than a Right Angle ; and that which is in the Segment ADC , being less than a ...

I say , the Angle which is in the Semicircle BAC is a Right Angle , that which is in

the Segment ABC being greater than a Semicircle , viz . the

**Angle ABC**, is lessthan a Right Angle ; and that which is in the Segment ADC , being less than a ...

Side 102

ET

equiangular to the

Right Line AH 1 23.1 . at the Point A , make + an

DEF .

ET

**ABC**be à Circle givefi , and D E F a given * 17.30 in the Circle**ABC**,equiangular to the

**Triangle**DEF . ... the Circle**ABC**in the Point A , and with theRight Line AH 1 23.1 . at the Point A , make + an

**Angle**HAC , equal to the**Angle**DEF .

Side 155

EGF ; and because the Angle DEF is equal to the Angle GEF ; and the Angle GEF

equal to the

Angle DF E ; as also the Angle A equal to the Angle D ; therefore the

EGF ; and because the Angle DEF is equal to the Angle GEF ; and the Angle GEF

equal to the

**Angle ABC**; therefore the ... the**Angle ACB**shall be equal to theAngle DF E ; as also the Angle A equal to the Angle D ; therefore the

**Triangle****ABC**... Side 156

Lgle of the one , equal to one

equal to the Bafe FG , and the

Anviz , the

...

Lgle of the one , equal to one

**Angle**of the other , Consequently the Base EF is *equal to the Bafe FG , and the

**Triangle**... ET two Triangles**ABC**, DEF , have oneAnviz , the

**Angle**BAC equal to the**Angle**EDF ; and let the Sides about the other...

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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.