## 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 |

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Resultat 1-5 av 5

Side 256

Cylinder ; and doing this continually , we shall at last have certain Portions of the

Cylinder left , that are less than the Excess by which the Cylinder exceeds triple

the

...

Cylinder ; and doing this continually , we shall at last have certain Portions of the

Cylinder left , that are less than the Excess by which the Cylinder exceeds triple

the

**Cone**. Now let these Portions remaining be AE , E B , BF , FC , CG , GD , DH...

Side 258

THE O - R E M.

their Bases . ... For if it be not so , it shall be as the Circle ABCD is to the Circle

EFGH , so is the

THE O - R E M.

**Cones**and Cylinders of the fame Altitude are to one another astheir Bases . ... For if it be not so , it shall be as the Circle ABCD is to the Circle

EFGH , so is the

**Cone**AL to some Solid either less or greater than the**Cone**EN . Side 259

Therefore the Pyramid remaining , whose Base is the Polygon HOEPFRGS , and

Altitude the fame as that of the

DTAYBQCV be described in the Circle ABCD , similar and alike fituate to the ...

Therefore the Pyramid remaining , whose Base is the Polygon HOEPFRGS , and

Altitude the fame as that of the

**Cone**, is greater than the Solid X. Let the PolygonDTAYBQCV be described in the Circle ABCD , similar and alike fituate to the ...

Side 260

Z is to the

And therefore as the Circle EFGH is to the Circle ABCD , fo is the

fome Solid less than the

Therefore ...

Z is to the

**Cone**AL , so is the**Cone**EN to some Solid less than the**Cone**AL .And therefore as the Circle EFGH is to the Circle ABCD , fo is the

**Cone**EN tofome Solid less than the

**Cone**AL ; which has been proved to be impoffible .Therefore ...

Side 263

But the

fuppofed to have to the Solid X a triplicate Proportion of that which BD has to FH .

Therefore as the

is to ...

But the

**Cone**whose Base is the Circle ABCD , and Vertex the Point L , isfuppofed to have to the Solid X a triplicate Proportion of that which BD has to FH .

Therefore as the

**Cone**, whose Base is the Circle ABCD , and Vertex the Point L ,is to ...

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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.