## 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

Side 85

THEORE M. Two similar and unequal

upon the same Right Line , and on the same ... Now because the

is similar to the

THEORE M. Two similar and unequal

**Segments**of two Circles , cannot be setupon the same Right Line , and on the same ... Now because the

**Segment**ACBis similar to the

**Segment**AD B , and similar**Segments**of Circles are * such * Def . Side 86

CD , the

Time that ... Therefore similar

are equal to one another ; which was to be demonstrated . PROPOSITION XXV .

CD , the

**Segment**AEB will co - incide with the**Segment**CFD . For if at the sameTime that ... Therefore similar

**Segments**of Circles being upon equal Right Lines ,are equal to one another ; which was to be demonstrated . PROPOSITION XXV .

Side 87

But if the Angle ABD be equal to the Angle BAD ; then if AD be made equal to BD

, or DC , the three Right Lines AD , DB , DC , are equal between themselves , and

D will be the Center of the Circle to be described ; and the

But if the Angle ABD be equal to the Angle BAD ; then if AD be made equal to BD

, or DC , the three Right Lines AD , DB , DC , are equal between themselves , and

D will be the Center of the Circle to be described ; and the

**Segment**ABC is á ... Side 91

TH EQRE M. In a Circle , the Angle that is in a Semicircle , is a Right Angle ; but

the Angle in a greater

leffer

TH EQRE M. In a Circle , the Angle that is in a Semicircle , is a Right Angle ; but

the Angle in a greater

**Segment**, is less than a Right Angle ; and the Angle in aleffer

**Segment**, greater than a Right Angle : Moreover , the Angle of a greater ... Side 92

will be greater than a Right Angle , and is in the

than a Semicircle . I say , moreover , the Angle of the greater

under the Circumference ABC , and the Right Line AC , is greater than a Right ...

will be greater than a Right Angle , and is in the

**Segment**ADC , which is lessthan a Semicircle . I say , moreover , the Angle of the greater

**Segment**containedunder the Circumference ABC , and the Right Line AC , is greater than a Right ...

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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.