## 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 66

THEOREM . if in a Circle a Right Line drawn thro ' the

Right Line not drawn throm the

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 otherRight 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 67

If in a Circle two Right Lines not being drawn tbro ' the

they will not cut each other into two equal Parts . L ET ABCD be a Circle , wherein

two Right Lines AC , BD , not drawn thro ' the

...

If in a Circle two Right Lines not being drawn tbro ' the

**Center**, cut each other ,they will not cut each other into two equal Parts . L ET ABCD be a Circle , wherein

two Right Lines AC , BD , not drawn thro ' the

**Center**, cut each other in the Point...

Side 68

Now because E is the

because E is the

shewn to be equal to EF . Therefore E F shall be equal to EG , a less to a greater

...

Now because E is the

**Center**of the Circle ABC , CE will be equal to EF . Again ,because E is the

**Center**of the Circle CDG , ČE is equal to E G. But CE has beenshewn to be equal to EF . Therefore E F shall be equal to EG , a less to a greater

...

Side 77

THEOREM . Equal Right Lines in a Circle are equally distant from the

and Right Lines , which are equally distant from the

themselves . L ET ABDC be a Circle , wherein are the equal Right Lines AB , CD .

THEOREM . Equal Right Lines in a Circle are equally distant from the

**Center**;and Right Lines , which are equally distant from the

**Center**, are equal betweenthemselves . L ET ABDC be a Circle , wherein are the equal Right Lines AB , CD .

Side 82

Therefore , if any Right Line touches a Circle , and from the

Contatt a Right Line be drawn ; that Line will be perpendicular to the Tangent ;

which was to be demonstrated . PROPOSITION XIX . 1 THEOREM . If any Right ...

Therefore , if any Right Line touches a Circle , and from the

**Center**to the point ofContatt a Right Line be drawn ; that Line will be perpendicular to the Tangent ;

which was to be demonstrated . PROPOSITION XIX . 1 THEOREM . If any Right ...

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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.