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 ... |
From inside the book
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Page 1
... Line are Points . IV . A Right Line is that which lieth evenly be- tween its Points . V. A Superficies is that which hath only Length and Breadth . VI . The Bounds of a Superficies are Lines . VII . A plane Superficies is that which ...
... Line are Points . IV . A Right Line is that which lieth evenly be- tween its Points . V. A Superficies is that which hath only Length and Breadth . VI . The Bounds of a Superficies are Lines . VII . A plane Superficies is that which ...
Page 2
... Line , called the Circumference ; to which all Right Lines , drawn from a certain Point within the Figure , are equal . XVI . And that Point is called the Centre of the Circle . XVII . A Diameter of a Circle is a Right Line drawn ...
... Line , called the Circumference ; to which all Right Lines , drawn from a certain Point within the Figure , are equal . XVI . And that Point is called the Centre of the Circle . XVII . A Diameter of a Circle is a Right Line drawn ...
Page 5
... Right Line . L ETAB be the given finite Right Line , upon which it is required to defcribe an equilateral Triangle . de- About the Centre A , with the Distance A B , fcribe the Circle B C D * ; and about the Centre B , * Poß . 3 . with ...
... Right Line . L ETAB be the given finite Right Line , upon which it is required to defcribe an equilateral Triangle . de- About the Centre A , with the Distance A B , fcribe the Circle B C D * ; and about the Centre B , * Poß . 3 . with ...
Page 6
... 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 unequal Right Lines being given to cut off a Part from 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 unequal Right Lines being given to cut off a Part from the ...
Page 7
... Right Line A B with DE , then the Point B. will co - incide with the Point E , 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 ...
... Right Line A B with DE , then the Point B. will co - incide with the Point E , 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 ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
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 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.
Page 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.
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 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.
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 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.