## 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 37

FCE ; for they are constituted upon equal Bases , and between the fame Parallels

BE , AF . But the Triángle ABC is equal to the Triangle D CE : Therefore D2

the Triangle DCE shall be equal to the Triangle Book I. Euclid's Ë L E MË NT $ .

FCE ; for they are constituted upon equal Bases , and between the fame Parallels

BE , AF . But the Triángle ABC is equal to the Triangle D CE : Therefore D2

**fore**the Triangle DCE shall be equal to the Triangle Book I. Euclid's Ë L E MË NT $ .

Side 40

Where

, thro ' which * draw KL parallel to EA , or FH , and produce AH , GB , to the Points

L and M. Therefore HLKF is a Parallelogram , whose Diameter is HK ; and AG ...

Where

**fore**HB , FE , produced , will meet each other ; whick 31 of this . let be in K, thro ' which * draw KL parallel to EA , or FH , and produce AH , GB , to the Points

L and M. Therefore HLKF is a Parallelogram , whose Diameter is HK ; and AG ...

Side 79

greater than F G. Wherefore the Diameter is the greatest Line in a Circle ; and of

all the other Lines therein , that which is nearest to the Center is greater than that

...

**fore**B C is greater than F G. And so the Diameter AD is the greatest , and B C isgreater than F G. Wherefore the Diameter is the greatest Line in a Circle ; and of

all the other Lines therein , that which is nearest to the Center is greater than that

...

Side 131

Therefore A is not equal to B : Neither is it less than B ; for then A would have t a

lefs Proportion to C than B would have ; but it hath not a lefs Proportion : ThereB

Therefore A is not equal to B : Neither is it less than B ; for then A would have t a

lefs Proportion to C than B would have ; but it hath not a lefs Proportion : ThereB

**fore**A is not less than B. But it has been proved likewise not to be equal to it ... Side 185

B A to AC , as CD to D Е , the Triangle ABC will be * equiangular to the Triangle

DCE ; where- * 6 of shiso

Angle ACD has been proved to be equal to the Angle BAC ; therefore the whole ...

B A to AC , as CD to D Е , the Triangle ABC will be * equiangular to the Triangle

DCE ; where- * 6 of shiso

**fore**the Angle A B C is equal to the Angle DCE ; but theAngle ACD has been proved to be equal to the Angle BAC ; therefore the whole ...

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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.