## 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 5

Side 106

Therefore ABCD is a rectangular quadrilateral Figure : But it has also been

described in the Circle ABCD ; which was to be done . PROPOSITION VII , 17. 3 .

+18.3 .

Therefore ABCD is a rectangular quadrilateral Figure : But it has also been

**proved**to be equilateral . Wherefore it shall necessarily be a Square , and isdescribed in the Circle ABCD ; which was to be done . PROPOSITION VII , 17. 3 .

+18.3 .

Side 112

Again , because BK has been

also HK the double of BK , HK shall be equal to KL . So likewise , we

GH , GM , and ML , are each equal to HK , or KL . Therefore the Pentagon ...

Again , because BK has been

**proved**equal to KC , and KL the double to K C , asalso HK the double of BK , HK shall be equal to KL . So likewise , we

**prove**thatGH , GM , and ML , are each equal to HK , or KL . Therefore the Pentagon ...

Side 115

Again , because the Point D is the Center of the Circle EGCH , DE shall be equal

to DG : But GE has been

so EGD is an equilateral Triangle ; ånd consequently the thrée Angles thereof ...

Again , because the Point D is the Center of the Circle EGCH , DE shall be equal

to DG : But GE has been

**proved**equal to GD . Therefore G E is equal to ED . Andso EGD is an equilateral Triangle ; ånd consequently the thrée Angles thereof ...

Side 170

But it has been

Triangle ABE is to the Triangle F GL : Therefore as the Triangle ABE is to the

Triangle F GL , fo is the Triangle BEC to the Triangle GHL ; and fo is the Triangle

ECD to ...

But it has been

**proved**, that the Triangle EBC is to the Triangle LGH , as theTriangle ABE is to the Triangle F GL : Therefore as the Triangle ABE is to the

Triangle F GL , fo is the Triangle BEC to the Triangle GHL ; and fo is the Triangle

ECD to ...

Side 194

Again , because A D is equal to CB , and AF to FB , the two Sides FA , AD , will be

equal to the two Sides FB , BC , each to each ; but the Bafe DF has been

equal to $ 8.5 . the Base FC : Therefore the Angle FAD is equal to the Angle ...

Again , because A D is equal to CB , and AF to FB , the two Sides FA , AD , will be

equal to the two Sides FB , BC , each to each ; but the Bafe DF has been

**proved**equal to $ 8.5 . the Base FC : Therefore the Angle FAD is equal to the Angle ...

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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.