## 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 44

Therefore the Square BE ,

Square

...

Therefore the Square BE ,

**described**on the Side B C , is equal to the Squares**described**on the Sides BA , AC . Wherefore in any Right - angled Triangle , theSquare

**described**upon the Side fubtending the Right Ångle , is equal to both the...

Side 104

Wherefore a Circle

, DF , DG , will also pass thro ' the other Points . And the sides AB , BC , AC , will

touch it ; because the Angles at E , F , and Gare Right Angles . For if it fhould cut ...

Wherefore a Circle

**described**about the Center D , with either of the Distances DE, DF , DG , will also pass thro ' the other Points . And the sides AB , BC , AC , will

touch it ; because the Angles at E , F , and Gare Right Angles . For if it fhould cut ...

Side 184

20. proportional , the first fhall be † to the third , as a Figure

to a similar and alike fituate Figure

to BD , fo is a Figure

20. proportional , the first fhall be † to the third , as a Figure

**described**on the first ,to a similar and alike fituate Figure

**described**on the second . Wherefore as CB isto BD , fo is a Figure

**described**on CB to a fimilar and alike situate Figure ... Side 233

THEOR E M. If four Right Lines be proportional , the solid Parallelepipedons

fimilar , and in like manner

Solid Parallelepipedons , being similar , and alike

then ...

THEOR E M. If four Right Lines be proportional , the solid Parallelepipedons

fimilar , and in like manner

**described**from them , all be proportional . And if theSolid Parallelepipedons , being similar , and alike

**described**, be proportional ,then ...

Side 270

... and the other Hemisphere , there will be conftituted a polyhedrous Figure

quadrilateral Figures , and the : Triangle YRX , being of the fame Order , and 19.

11 .

... and the other Hemisphere , there will be conftituted a polyhedrous Figure

**described**in the Sphere , composed of Pyramids whose Bases are the aforesaidquadrilateral Figures , and the : Triangle YRX , being of the fame Order , and 19.

11 .

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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.