## 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 36

But the

Diameter AB bifects it ; and the Triangle DBC is one ... Wherefore , Triangles

constituted upon the fame Bafe , and between the same Parallels , are equal

between ...

But the

**Triangle A B C**is tone half of the Parallelogram EBCA , because theDiameter AB bifects it ; and the Triangle DBC is one ... Wherefore , Triangles

constituted upon the fame Bafe , and between the same Parallels , are equal

between ...

Side 149

PROPOSITION I. L TH É O R E M. Triangles and Parallelograms that have the

famë Altitude , are to each other as their ... I say , as the Base BC , is to the Base

CD , so is the

EC ...

PROPOSITION I. L TH É O R E M. Triangles and Parallelograms that have the

famë Altitude , are to each other as their ... I say , as the Base BC , is to the Base

CD , so is the

**Triangle ABC**, to the Triangle ACD , and so is the ParallelogramEC ...

Side 150

N3 And because the Parallelogram EC , is † double to the

Parallelogram FC , double † to the Triangle A CD ; and Parts have the same

Proportion as their like Multiples . Therefore as the

Triangle ...

N3 And because the Parallelogram EC , is † double to the

**Triangle ABC**; and theParallelogram FC , double † to the Triangle A CD ; and Parts have the same

Proportion as their like Multiples . Therefore as the

**Triangle A B C**is to theTriangle ...

Side 158

If a Perpendicular be drawn , in a Right - lined

the Base , then the

to the whole , and also to one another . ET

If a Perpendicular be drawn , in a Right - lined

**Triangle**, from the Right Angle tothe Base , then the

**Triangles**on each side of the Perpendicular are similar bothto the whole , and also to one another . ET

**ABC**be a Right - angled**Triangle**... Side 163

But as the Triangle CAB is to the Triangle BAD , so is CA Ito AD , and as the Tri- II

of this . angle EAD is to the Triangle BAD , fo is I EA to AB . Therefore as CA is to

AD , so is EA to AB . Wherefore the sides of the

But as the Triangle CAB is to the Triangle BAD , so is CA Ito AD , and as the Tri- II

of this . angle EAD is to the Triangle BAD , fo is I EA to AB . Therefore as CA is to

AD , so is EA to AB . Wherefore the sides of the

**Triangles ABC**, ADE , about the ...### Hva folk mener - Skriv en omtale

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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.