## 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 7

Side 118

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

and third , and

Multiple of the first be greater than the Multiple of the second , and

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 theMultiple of the first be greater than the Multiple of the second , and

**also**theMultiple of ...

Side 139

Therefore , if Magnitudes compounded , are proportional ; they shall

proportional when divided ; which was to be demonstrated . PROPOSITION XVIII

. A THEOREM . If Magnitudes divided be proportional , the same

Therefore , if Magnitudes compounded , are proportional ; they shall

**also**beproportional when divided ; which was to be demonstrated . PROPOSITION XVIII

. A THEOREM . If Magnitudes divided be proportional , the same

**also**being ... Side 199

THE ORI M. Right Lines that are parallel to the same Right Line , not being in the

fame Plane with it , are

CD , be parallel to the Right Line EF , not being in the same Plane with it .

THE ORI M. Right Lines that are parallel to the same Right Line , not being in the

fame Plane with it , are

**also**parallel to each other . ET both the Right Lines AB ,CD , be parallel to the Right Line EF , not being in the same Plane with it .

Side 211

85. to And so the three Angles ABC , DEF , GHK , Ihall

Right Angles ; but they are put less than four Right Angles , which is absurd .

Therefore AB is not equal to LX . I say

...

85. to And so the three Angles ABC , DEF , GHK , Ihall

**also**be equal to four .Right Angles ; but they are put less than four Right Angles , which is absurd .

Therefore AB is not equal to LX . I say

**also**it is neither less than LX ; ' for if this be...

Side 230

Therefore HK shall * 8 of this . be *

BAC . Draw from the Points K , N , to the Right Lines AB , AC , DE , DF , the

Perpendiculars KB , KC , NE , NF , and join HC , CB , MF , FE . Then because +

47.

Therefore HK shall * 8 of this . be *

**also**perpendicular to the Plane passing thro 'BAC . Draw from the Points K , N , to the Right Lines AB , AC , DE , DF , the

Perpendiculars KB , KC , NE , NF , and join HC , CB , MF , FE . Then because +

47.

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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.