## 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 25

Therefore AB is not unequal to DE , and

two Sides AB , BC , are each equal to the two Sides DE , EF , and the Angle ABC

equal to the Angle DEF : And

DF ...

Therefore AB is not unequal to DE , and

**consequently**is equal to it . And so thetwo Sides AB , BC , are each equal to the two Sides DE , EF , and the Angle ABC

equal to the Angle DEF : And

**consequently**the Base AC * is equal to the BaseDF ...

Side 157

Therefore as AB is to BC , so is * By Hype AB to BG ; and since AB has the same

Proportion to BC , that it has to BG , BC shall be + equal to 1 9 : 5BG ; and

Angles ...

Therefore as AB is to BC , so is * By Hype AB to BG ; and since AB has the same

Proportion to BC , that it has to BG , BC shall be + equal to 1 9 : 5BG ; and

**consequently**the Angle at C equal to the Angle BGC . Wherefore each of theAngles ...

Side 167

Therefore the Triangle FDE , is equiangular to the Triangle GBH ; and

has been proved that FD is to GB , as FC is to GA , and as CD to AB . And

therefore as F C ...

Therefore the Triangle FDE , is equiangular to the Triangle GBH ; and

**consequently**, as FD is to GB , so is I F E to 4 of this . GH ; and so ED to HB . But ithas been proved that FD is to GB , as FC is to GA , and as CD to AB . And

therefore as F C ...

Side 266

Therefore the Base ABCD is equal to the Base E F G H. And

the Base ABCD is to the Base EFGH , so is the Altitude MN to the Altitude KL . But

1 But if the Altitude KL be not equal to the 266 Euclid's ELEMENT $ . Book XII .

Therefore the Base ABCD is equal to the Base E F G H. And

**consequently**, asthe Base ABCD is to the Base EFGH , so is the Altitude MN to the Altitude KL . But

1 But if the Altitude KL be not equal to the 266 Euclid's ELEMENT $ . Book XII .

Side 358

But to return ; if the Series expressing the Length of the Arch , viz . stý s + 4 s ' , &

c . be revers'd , we shall have the Value of s in the Terms of a , and

a direct Method for finding the Sine of any Arch from its Length given . Thus .

But to return ; if the Series expressing the Length of the Arch , viz . stý s + 4 s ' , &

c . be revers'd , we shall have the Value of s in the Terms of a , and

**consequently**a direct Method for finding the Sine of any Arch from its Length given . Thus .

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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.