## 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 8

Side 146

EH ; it

Magnitudes , being divided , † 18 of this are proportional , they

proportional when compounded . Therefore , as AG is to GB , fo is DH Hyp to HE :

But as ...

EH ; it

**shall**be * by Equality as A B is to BG , fo is DE to EH . And becauseMagnitudes , being divided , † 18 of this are proportional , they

**shall**also betproportional when compounded . Therefore , as AG is to GB , fo is DH Hyp to HE :

But as ...

Side 209

... HK , each to each and they contain equal Angles , the Base AL Ihall be equal

to the Base GK . And since the Angles E and H are greater than the Angle ABC ,

whereof the Anz gle GHK is equal to the Angle AB L , the other Angle at E

be ...

... HK , each to each and they contain equal Angles , the Base AL Ihall be equal

to the Base GK . And since the Angles E and H are greater than the Angle ABC ,

whereof the Anz gle GHK is equal to the Angle AB L , the other Angle at E

**shall**be ...

Side 270

Let the said Perpendiculars be OV , SQ , and join VQ . Then fince the equal

Circumferences BO , SK , are taken in the equal Semicircles BXD , KXN , and OV

, SQ are Perpendiculars , OV

B A ...

Let the said Perpendiculars be OV , SQ , and join VQ . Then fince the equal

Circumferences BO , SK , are taken in the equal Semicircles BXD , KXN , and OV

, SQ are Perpendiculars , OV

**shall**be equal to SQ , and B V to KQ . But the WholeB A ...

Side 288

Produce AB to H , so that BH = BC , then

you make BI = BA , then IH will be the Difference of the Legs . Also the Angle

HBC = Angles A + ACB , ( by 32. El . 1. ) and so EBCthe half thereof = half the

Sum ...

Produce AB to H , so that BH = BC , then

**shall**AH be the Sum of the Legs ; and ifyou make BI = BA , then IH will be the Difference of the Legs . Also the Angle

HBC = Angles A + ACB , ( by 32. El . 1. ) and so EBCthe half thereof = half the

Sum ...

Side 296

PROPOSITION XIII , In any spherical Triangle ABC , if the Sum of the Legs AB

and BC be greater , equal , or less , than a Semicircle , then the internal Angle at

the Base AC

PROPOSITION XIII , In any spherical Triangle ABC , if the Sum of the Legs AB

and BC be greater , equal , or less , than a Semicircle , then the internal Angle at

the Base AC

**shall**be greater , & qual , or less , than the external and opposite ...### Hva folk mener - Skriv en omtale

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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.