## 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 49

, shall be Right Angles . Therefore CGKB is a Rectangle . But it has been proved

to be equilateral . Therefore CGKB is a Square defcribed upon BC . BC .

**Wherefore**GBC also is a Right Angle , and the opposite Angles GCB , CGK , GKB, shall be Right Angles . Therefore CGKB is a Rectangle . But it has been proved

to be equilateral . Therefore CGKB is a Square defcribed upon BC . BC .

Side 57

But Right Lines making , with a third Line , Angles together less than two Right

Angles , being infinitely produced , will meet *

duced , will meet towards BD , Now let them be produced , and meet each other

in ...

But Right Lines making , with a third Line , Angles together less than two Right

Angles , being infinitely produced , will meet *

**Wherefore**EB , FD , pro- * Ax . 12 .duced , will meet towards BD , Now let them be produced , and meet each other

in ...

Side 184

situate Figure described on BĄ . For the fame Reason as BC is to CD , fo is a

Figure de fcribed on BC to one described on CA.

is to ...

**Wherefore**as CB is to BD , fo is a Figure described on CB to a fimilar and alikesituate Figure described on BĄ . For the fame Reason as BC is to CD , fo is a

Figure de fcribed on BC to one described on CA.

**Wherefore**1 24. 5 . also , as BCis to ...

Side 195

Angles in the common Section , it shall be also at Right Angles to the Plane

drawn thro ' the said Lines ; which was to be demonstrated . PROPOSITION V.

THE OR E ...

**Wherefore**, if to two Right Lines cutting one another , a third stands at RightAngles in the common Section , it shall be also at Right Angles to the Plane

drawn thro ' the said Lines ; which was to be demonstrated . PROPOSITION V.

THE OR E ...

Side 241

BOCPDR to * the Polygon EKFLGMHN . ...

greater than the Polygon EKFLGMHN , but it is less ft From that likewise , which is

...

**Wherefore**as the Square of B D is to the Square of FH , so is the Polygon AXBOCPDR to * the Polygon EKFLGMHN . ...

**Wherefore**the Space S shall be t alsogreater than the Polygon EKFLGMHN , but it is less ft From that likewise , which is

...

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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.