## 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 |

### Dentro del libro

Resultados 1-5 de 93

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**likewife**of Ufe in other Matters . not Notwithstanding this , Barrow's Demon- ftrations are fo very short , and are involved in fo many Notes and Symbols , that they are rendered cbfcure and difficult to one verfed in Geometry . There ... Página 6

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**likewife**A L is equal to B C. ↑ Ax . 3 . * Ax , I. Whence the Right Line A L is put at the given Point A , equal to the given Right Line B C , which was to be done . 2 of this . + Poft . 3 . + Ax . 1 . PROPOSITION III . PROBLEM . Two ... Página 7

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**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 , because the Right Line A C is equal to the Right Line D F. But the Point B co incides ... Página 9

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**likewife**been proved , that the Angles FBC , GCB , under the Bafe , are equal ; therefore , the Angles at the Bafe of Ifoceles Triangles are equal between themfelves ; and if the equal Right Lines be produced , the Angles under the Bafe ... Página 11

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**likewife**co incide with E D and D F. For if the Bafe B C fhould co - incide with E E , and at the fame Time the Sides B A , A C , fhould not co - incide with the Sides E D , DF , but change their Pofition , as EG , GF , then there would ...### 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.