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 Seiten |
Im Buch
Ergebnisse 1-5 von 100
Seite 4
... equal to one and the fame Thing , are equal to one another . II . If to equal Things are added equal Things , the Wholes will be equal . III . If from equal Things equal Things be taken away , the Remainders will be equal . IV . If equal ...
... equal to one and the fame Thing , are equal to one another . II . If to equal Things are added equal Things , the Wholes will be equal . III . If from equal Things equal Things be taken away , the Remainders will be equal . IV . If equal ...
Seite 6
... equal to the Whole DG , the Parts whereof DA and DC are equal ; therefore the Remainders A L , CG , are alfo equal ‡ . But it has been demon- ftrated , that BC is equal to CG ; wherefore both A L and BC are each of them equal to CG ...
... equal to the Whole DG , the Parts whereof DA and DC are equal ; therefore the Remainders A L , CG , are alfo equal ‡ . But it has been demon- ftrated , that BC is equal to CG ; wherefore both A L and BC are each of them equal to CG ...
Seite 7
... equal to two Sides of the other , each to each , and the Angle contained by thofe equal Sides in one Triangle , equal to the Angle contained by the correfpondent Sides in the other Triangle ; then the Bafe of one of the Triangles fhall be ...
... equal to two Sides of the other , each to each , and the Angle contained by thofe equal Sides in one Triangle , equal to the Angle contained by the correfpondent Sides in the other Triangle ; then the Bafe of one of the Triangles fhall be ...
Seite 8
... equal to them , viz . the Angle A B C equal to the Angle DE F , and the Angle ACB equal to the Angle D F E ; which was to be demonftrated . PROPOSITION V. THEOREM . The Angles at the Bafe of an Ifoceles Triangle are equal between ...
... equal to them , viz . the Angle A B C equal to the Angle DE F , and the Angle ACB equal to the Angle D F E ; which was to be demonftrated . PROPOSITION V. THEOREM . The Angles at the Bafe of an Ifoceles Triangle are equal between ...
Seite 9
... equal to the remaining Angles of the other , each to each , which fubtend the equal fides . And fo the An- gle FBC is equal to the Angle G CB ; and the Angle BCF equal to the Angle CB G. Therefore , because the whole Angle A BG hath ...
... equal to the remaining Angles of the other , each to each , which fubtend the equal fides . And fo the An- gle FBC is equal to the Angle G CB ; and the Angle BCF equal to the Angle CB G. Therefore , because the whole Angle A BG hath ...
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.