## 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 200

PROBLEM , From a Point given ałote a Plarie , to draw a Right Line

Plane BH . It is required to draw a Right Line from the Point A ,

the Plane BH .

PROBLEM , From a Point given ałote a Plarie , to draw a Right Line

**perpendicular**to that Plane . L 12. 1 . ET A be a Point given above the givenPlane BH . It is required to draw a Right Line from the Point A ,

**perpendicular**tothe Plane BH .

Side 201

Therefore GH is

likes wise is

But if a Right Line stands at Right Angles to two Right Lines , in their common ...

Therefore GH is

**perpendicular**to AF , and so AF is**perpendicular**to GH ; but AFlikes wise is

**perpendicular**to DE ; therefore AF is**perpendicular**to both HG , DE .But if a Right Line stands at Right Angles to two Right Lines , in their common ...

Side 206

1 which let FG be drawn in the Plane DE ,

Then because AB is • Def . 3.

1 which let FG be drawn in the Plane DE ,

**perpendicular**to the Right Line CE .Then because AB is • Def . 3.

**perpendicular**to the Plane CL , it shall also be ***perpendicular**to all the Right Lines which touch it , and are in the fame Plane . Side 234

If a Plane be

of the Planes

common Section of the Planes . * Def : ET the Plane CD be

If a Plane be

**perpendicular**to a Plane , and a Line bé drawn from a Point in oneof the Planes

**perpendicular**to the other Plane , that**Perpendicular**fəall fall in thecommon Section of the Planes . * Def : ET the Plane CD be

**perpendicular**to the ... Side 300

In any Spherical Triangle ABC , if the Angles at the Base B and C , be of the same

Affection , then the

different Affection , the

if ...

In any Spherical Triangle ABC , if the Angles at the Base B and C , be of the same

Affection , then the

**Perpendicular**falls within the Triangle ; and if they be of adifferent Affection , the

**Perpendicular**falls without the Triangle . IN the first Case ,if ...

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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.