## 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 8

Side 169

Now

one Angle of the other , and the Sides about the equal Angles proportional ; the

Triangle A BE will be * equiangular * 6 of this . to the Triangle FĞL ; and also ...

Now

**since**ABE , FGL , are two Triangles , having one Angle of the one equal toone Angle of the other , and the Sides about the equal Angles proportional ; the

Triangle A BE will be * equiangular * 6 of this . to the Triangle FĞL ; and also ...

Side 175

Then because B C is to CG as the Parallelogram AC is * to the Parallelogram CH

: And

so is the Parallelogram AC , to the Parallelogram CH . Again , because DC is to ...

Then because B C is to CG as the Parallelogram AC is * to the Parallelogram CH

: And

**since*** 1 of this . BC is to CG as K is to L , it shall be f as K is to L , † 11. s .so is the Parallelogram AC , to the Parallelogram CH . Again , because DC is to ...

Side 198

And

CDB , +29 . 1 . fhall be + equal to two Right Angles . Therefore the Angle CDB is

also a Right Angle , and so CD iş perpendicular to DB : And

...

And

**since**the Right Line BD falls on the Right Lines AB , CD , the Angles A BD ,CDB , +29 . 1 . fhall be + equal to two Right Angles . Therefore the Angle CDB is

also a Right Angle , and so CD iş perpendicular to DB : And

**since**AB is equal to...

Side 209

Then , because the two Sides AB , BL , are equal to the two Sides GH , HK , each

to each and they contain equal Angles , the Base AL Ihall be equal to the Base

GK . And

...

Then , because the two Sides AB , BL , are equal to the two Sides GH , HK , each

to each and they contain equal Angles , the Base AL Ihall be equal to the Base

GK . And

**since**the Angles E and H are greater than the Angle ABC , whereof the...

Side 231

And

DM ; but the Squares of A K , KH , are equal to the Square of AH ; for the Angle A

KH is a Right Angle , and the Squares DN , NM , are equal to the Square of DM ...

And

**since**AH is equal to DM , the Square of A H shall be equal to the Square ofDM ; but the Squares of A K , KH , are equal to the Square of AH ; for the Angle A

KH is a Right Angle , and the Squares DN , NM , are equal to the Square of DM ...

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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.