## 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 7

Side 118

That is , if there be four Magnitudes , and you take any Equimultiples of the

and third , and also any Equimultiples of the second and fourth . And if the

Multiple of the

Multiple of ...

That is , if there be four Magnitudes , and you take any Equimultiples of the

**first**and third , and also any Equimultiples of the second and fourth . And if the

Multiple of the

**first**be greater than the Multiple of the second , and also theMultiple of ...

Side 135

If the

and if the

fourth . But if the

If the

**first**has the same Proportion to the second , as the third bas to the fourth ;and if the

**first**be greater than the third ; then will the second be greater than thefourth . But if the

**first**be equal to the third , then the second hall be equal to the ... Side 174

If any four Right Lines A , B , C , and D , be proposed , the Ratio of the

the fourth D , is equal to the Ratia compounded of the Ratio of the firft A to the

second B , and of the Ratio of the second B to the third C , and of the Ratio of the

third ...

If any four Right Lines A , B , C , and D , be proposed , the Ratio of the

**first**A tothe fourth D , is equal to the Ratia compounded of the Ratio of the firft A to the

second B , and of the Ratio of the second B to the third C , and of the Ratio of the

third ...

Side 334

... Numbers which , being adjoined to Proportions , have equal Differenccs . In the

Proportionals was placed only fo far diftant from Unity , as that Term exceeded

Unity .

... Numbers which , being adjoined to Proportions , have equal Differenccs . In the

**first**Kind of Logarithms that Neper publifh'd , the**first**Term of the continualProportionals was placed only fo far diftant from Unity , as that Term exceeded

Unity .

Side 347

to the Logarithm of the

But if a Series of Proportionals be decreasing , that is , if the Terms diminish in a

continual Ratio , and Q n be the

...

to the Logarithm of the

**first**Term , then will the Logarithm of that Term be had :But if a Series of Proportionals be decreasing , that is , if the Terms diminish in a

continual Ratio , and Q n be the

**first**Term ; then the Logarithm of any other will be...

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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.