## 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 6

Side 15

THEORE M. If one side of any Triangle be

greater than either of the inward opposite ... and join BE , which pro- * 10 of this ,

duce to F , and make E F equal to B E. Moreover , join F C , and

.

THEORE M. If one side of any Triangle be

**produced**, the outward Angle isgreater than either of the inward opposite ... and join BE , which pro- * 10 of this ,

duce to F , and make E F equal to B E. Moreover , join F C , and

**produce**A C to G.

Side 26

For if it be not parallel , AB and CD ,

and C , will meet : Now let them be

Point G. Then the outward Angle AEF of the Triangle 3-6 óf ibis . GEF , is * greater

...

For if it be not parallel , AB and CD ,

**produced**towards B and D , or towards Aand C , will meet : Now let them be

**produced**towards B and D , and meet in thePoint G. Then the outward Angle AEF of the Triangle 3-6 óf ibis . GEF , is * greater

...

Side 40

BEFG equal to * the Triangle C ; in the Angle EBG , equal to D. Place BE in a

straight Line with AB , and

two Right Angles , with a third Line being infinitely

other .

BEFG equal to * the Triangle C ; in the Angle EBG , equal to D. Place BE in a

straight Line with AB , and

**produce**FG to H ... but Right Lines making less thantwo Right Angles , with a third Line being infinitely

**produced**, will meet * eachother .

Side 173

Number 3 be the Exponent , or Denominator of the Ratio of A to B ; that is , let A

be three times B , and let the Number be the Exponent of the Ratio of B to C ; then

the Number 12

Number 3 be the Exponent , or Denominator of the Ratio of A to B ; that is , let A

be three times B , and let the Number be the Exponent of the Ratio of B to C ; then

the Number 12

**produced**by the Multiplication of 4 and 3 , is the compounded ... Side 204

I lay EF is parallel to GH . For if it is not parallel , EF , GH , being

meet each other either on the Side FH , or EG . First let them be

Side EH , and meet in K ; then because EFK is in the Planę AB , all Points taken

in ...

I lay EF is parallel to GH . For if it is not parallel , EF , GH , being

**produced**, willmeet each other either on the Side FH , or EG . First let them be

**produced**on theSide EH , and meet in K ; then because EFK is in the Planę AB , all Points taken

in ...

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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.