## Euclid's Elements of Geometry: From the Latin Translation of Commandine, to which is Added, a Treatise of the Nature and Arithmetic of Logarithms ; Likewise Another of the Elements of Plane and Spherical Trigonometry ; with a Preface ... |

### Inni boken

Resultat 1-5 av 7

Side 73

We prove ,, in the same

the greatest of the Right Lines falling from the Point D ; DE is greater than DF ,

and D F is greater than DC . Moreover , because MK and KD are * greater than

MD ...

We prove ,, in the same

**manner**, that FD is greater than CD . Wherefore , D A isthe greatest of the Right Lines falling from the Point D ; DE is greater than DF ,

and D F is greater than DC . Moreover , because MK and KD are * greater than

MD ...

Side 99

Ta LET fome Port D be affumed without the Circle ABC , and from it draw two

Right Lines DCA , D B , to che Circle , in such a

, and D B falls upon it : And let the Rectangle under A D and D C be equal to the ...

Ta LET fome Port D be affumed without the Circle ABC , and from it draw two

Right Lines DCA , D B , to che Circle , in such a

**manner**, that DCA cuts the Circle, and D B falls upon it : And let the Rectangle under A D and D C be equal to the ...

Side 107

In this

G F is parallel to H K. Therefore GK , GC , AK , F B , BK , + 34. 1 . are

Parallelograms ; and fo GF + is equal to HK , and GH to FK . And since AC is

equal to BD , and ...

In this

**manner**we prove likewise , that GF and H K are parallel to BED ; and soG F is parallel to H K. Therefore GK , GC , AK , F B , BK , + 34. 1 . are

Parallelograms ; and fo GF + is equal to HK , and GH to FK . And since AC is

equal to BD , and ...

Side 240

If the Halves of the Magnitudes thould have been taken , we demonstrate this

after the fame

PROPOSITION II . THEOREM . Circles are to each other as the Squares of their

Diameters .

If the Halves of the Magnitudes thould have been taken , we demonstrate this

after the fame

**manner**. This is the first Proposition of the tenth Book .PROPOSITION II . THEOREM . Circles are to each other as the Squares of their

Diameters .

Side 299

In like

Circle TMN , the Arcs DN , HN , will be Quadrants ; and so ( by Cor . 2. Prop . 3. )

N thall be the Pole of the Circle HD . And because GX , D X , are Quadrants , X ...

In like

**manner**, because D is the Pole of the Circle X BN , and H the Pole of theCircle TMN , the Arcs DN , HN , will be Quadrants ; and so ( by Cor . 2. Prop . 3. )

N thall be the Pole of the Circle HD . And because GX , D X , are Quadrants , X ...

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### Vanlige uttrykk og setninger

A B C ABCD added alſo Altitude Bale Baſe becauſe Centre Circle Circumference common Cone conſequently contained Cylinder demonſtrated deſcribed Diameter Difference Diſtance divided double draw drawn equal equal Angles equiangular exceeds fall fame fince firſt fore four fourth given greater half ibis join leſs likewiſe Logarithm Magnitudes manner Multiple Number oppoſite parallel Parallelogram perpendicular Place Plane Point Polygon Priſm produced Prop Proportion PROPOSITION proved Pyramid Quadrant Ratio Reaſon Rectangle remaining Right Angles Right Line Right Line A B ſaid ſame ſay ſecond Segment Series ſhall ſhall be equal Sides ſimilar ſince Sine Solid ſome Sphere Square taken tbis Terms THEOREM thereof theſe third thoſe thro touch Triangle Unity Whence Wherefore whole whoſe Baſe

### Populære avsnitt

Side 193 - 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 xxiii - If two triangles have two sides of the one equal to two sides of the other, each to each ; and have likewise the angles contained by those sides equal to each other; they shall likewise have their bases, or third sides, equal; and the two triangles shall be equal; and their other angles shall be equal, each to each, viz. those to which the equal sides are opposite.

Side 236 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 11 - ... 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 equal to DE, and AC to DF ; but...

Side 85 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Side 147 - A straight line is said to be cut in extreme and mean ratio, when the whole is to the greater segment as the greater segment is to the less.

Side 50 - CB, and to twice the rectangle AC, CB: but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB ; therefore the square of AB is equal to the squares of AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line be divided, &c.

Side xxv - EF (Hyp.), the two sides GB, BC are equal to the two sides DE, EF, each to each. And the angle GBC is equal to the angle DEF (Hyp.); Therefore the base GC is equal to the base DF (I.

Side xxxiv - ... therefore their other sides are equal, each to each, and the third angle of the one to the third angle of the other (26.

Side 194 - ABC, and they are both in the same plane, which is impossible ; therefore the straight line BC is not above the plane in which are BD and BE: wherefore, the three straight lines BC, BD, BE are in one and the same plane. Therefore, if three straight lines, &c.