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 ... |
Common terms and phrases
A B C adjacent Angles alfo alſo equal Altitude Angle ABC Angle BAC Bafe becauſe biſected Centre Circle ABCD Circumference Cofine Cone conſequently Coroll Cylinder demonftrated deſcribed Diameter Diſtance drawn equal Angles equiangular equilateral Equimultiples faid fame Multiple fame Proportion fame Reaſon fimilar fince firſt folid Parallelopipedon fore fubtending given Right Line greater join leſs likewiſe Logarithm Magnitudes Meaſure Number oppofite parallel Parallelogram perpendicular Polygon Priſm Prop PROPOSITION Pyramid Quadrant Ratio Rectangle Rectangle contained remaining Angle Right Angles Right Line A B Right-lined Figure ſame ſay ſecond Segment Semicircle ſhall be equal Sides ſince Sine Solid ſome Sphere Square ſtand Subtangent THEOREM thereof theſe thoſe thro tiple Triangle ABC Unity Vertex the Point Whence Wherefore whole whoſe Baſe
Popular passages
Page 195 - 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.
Page 22 - 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.
Page 238 - 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.
Page 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...
Page 87 - 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.
Page 149 - 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.
Page 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.
Page 22 - 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.
Page 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.
Page 196 - 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.