## 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 74

For

which produce to the Points H , K , O , L ; then because A E is equal to E B , and

ED is common , the two Sides AE , ED , shall be equal to the two Sides BE , ED .

For

**join**AB , BC , which bisect * in the Points E and Ž ; as also**join**ED , DZ ;which produce to the Points H , K , O , L ; then because A E is equal to E B , and

ED is common , the two Sides AE , ED , shall be equal to the two Sides BE , ED .

Side 90

For find * the Centers of the Circles K , L , and

because the Circumference BGC is equal to the Circumference EHF ; the Angle

BKC shall be +27 of tbis . t equal to the Angle ELF . And because the Circles ABC

, DEF ...

For find * the Centers of the Circles K , L , and

**join**BK , KC , EL , LF . Thenbecause the Circumference BGC is equal to the Circumference EHF ; the Angle

BKC shall be +27 of tbis . t equal to the Angle ELF . And because the Circles ABC

, DEF ...

Side 105

Therefore describe the Circle ABC .; Secondly , let DF , EF , meet each other in

the Point F , in the Side BC , as in the second Figure , and

prove , as before , that the Point F is the Center of a Circle described about the

Triangle ...

Therefore describe the Circle ABC .; Secondly , let DF , EF , meet each other in

the Point F , in the Side BC , as in the second Figure , and

**join**AF . Then weprove , as before , that the Point F is the Center of a Circle described about the

Triangle ...

Side 217

Lastly , make A K equal to DG , and at the Point K erect | HK at Right Angles to

the Plane passing # 12 of this thro ' BAL , and make KĦ equal to GF , and

. I say , the solid Angle at A , which is contained under the three plane Angles

BAL ...

Lastly , make A K equal to DG , and at the Point K erect | HK at Right Angles to

the Plane passing # 12 of this thro ' BAL , and make KĦ equal to GF , and

**join**HA. I say , the solid Angle at A , which is contained under the three plane Angles

BAL ...

Side 270

Let those Sides be BO , OP , PR , RX , KS , ST , TY , YX : And

and let Perpendiculars be drawn from O , S , to the Plane of the Circle BCDE ,

There will † fall on BD , KN , the common Sections of the Planes ; because the ...

Let those Sides be BO , OP , PR , RX , KS , ST , TY , YX : And

**join**SO , TP , YR ;and let Perpendiculars be drawn from O , S , to the Plane of the Circle BCDE ,

There will † fall on BD , KN , the common Sections of the Planes ; because the ...

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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.