## 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

Right Line not drawn throm the Center , into equal Parts , it fall cut it at Right

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 Right

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

be a ...

Side 67

L ET ABCD be a Circle , wherein two Right Lines AC , BD , not drawn

Center , cut each other in the Point E. I say , they do not bisect each other . For , if

possible , let them bisect each other , so that AE be equal to EC , and BE to ED .

L ET ABCD be a Circle , wherein two Right Lines AC , BD , not drawn

**thro**' theCenter , cut each other in the Point E. I say , they do not bisect each other . For , if

possible , let them bisect each other , so that AE be equal to EC , and BE to ED .

Side 195

Wherefore , if to two Right Lines cutting one another , a third stands at Right

Angles in the common Section , it shall be also at Right Angles to the Plane

drawn

THE OR E ...

Wherefore , if to two Right Lines cutting one another , a third stands at Right

Angles in the common Section , it shall be also at Right Angles to the Plane

drawn

**thro**' the said Lines ; which was to be demonstrated . PROPOSITION V.THE OR E ...

Side 199

For affume any Point Gin EF , from which Point G , let GH be drawn at Right

Angles to E F , in the Plane paffing

Angles to E F in the Plane passing

perpendicular ...

For affume any Point Gin EF , from which Point G , let GH be drawn at Right

Angles to E F , in the Plane paffing

**thro**' EF , AB : Also let GK be drawn at RightAngles to E F in the Plane passing

**thro**” EF , CD : Then because EF isperpendicular ...

Side 203

PROPOSITION XV , THEOREM , If two Right Lines , touching one another , be

parallel to two Right Lines , touching one anotber , and not being in the same

Plane with them , the Planes drawn

otber .

PROPOSITION XV , THEOREM , If two Right Lines , touching one another , be

parallel to two Right Lines , touching one anotber , and not being in the same

Plane with them , the Planes drawn

**thro**' those Right Lines are parallel to eachotber .

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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.