## 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 ...W. Strahan, 1782 - 399 páginas |

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**because**expounded in one and the fame Plane , as the first fix . Elements were , claimed , by a Right Or- . der to be handled before Planes inter- fected by Planes , or the more compounded Doctrine of Solids ; and the Properties of ... Página 6

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**because**the Point C is the Centre of the Circle Def . 15. BGH , BC will be equal to CG + ; and**because**D is the Centre of the Circle K GL , the Whole D L will be equal to the Whole DG , the Parts whereof DA and DC are equal ; therefore ... Página 7

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**because**A B is equal to D E. And fince A B co - incides with D E , the Right Line A C likewife will co - incide with the Right Line D F , be- caufe the Angle B A C is equal to the Angle ED F. Wherefore alfo C will co - incide with F , ... Página 8

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**because**AF is equal to AG , and AB to AC , the two Right Lines F A , A C , are equal to the two Lines GA , A B , each to each , and contain the com- * 4 of this . mon Angle F AG ; therefore the Base F C is equal + to the Bafe G B , and ... Página 10

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**because**A C is equal to AD , the Angle 15 of this . ACD will be equai + to the Angle ADC , and con- fequently the Angle A D C is greater than the Angle BCD ; wherefore the Angle BDC will be much greater than the Angle B CD . Again ,**because**...### Términos y frases comunes

ABCD adjacent Angles alfo equal alſo Angle ABC Baſe becauſe bifected Centre Circle A B C Circumference Cofine Cone confequently Cylinder defcribed demonftrated Diameter Diſtance drawn equal Angles equiangular Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reafon fecond fhall be equal fimilar fince firft folid Parallelopipedon fome fore ftand fubtending given Right Line Gnomon join leffer lefs likewife Logarithm Magnitudes Meaſure Number parallel Parallelogram perpendicular Polygon Prifm Prop PROPOSITION Pyramid Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure Segment Semicircle ſhall Sides A B Sine Solid Sphere Square Subtangent thefe THEOREM thofe thro tiple Triangle ABC Unity Vertex the Point Wherefore whofe Bafe

### Pasajes populares

Página 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.

Página 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.

Página 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.

Página 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...

Página 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.

Página 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.

Página 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.

Página 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.

Página 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.

Página 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.