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 |
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... four Books , viz . the ift of the 10th , is quoted in the 11th and 12th Books ; and that only twice , viz . in the Demonftration of the 2d and 16th of the 12th ; and that ift Propofition of the 19th is fupplied by a Lemma in the 12th ...
... four Books , viz . the ift of the 10th , is quoted in the 11th and 12th Books ; and that only twice , viz . in the Demonftration of the 2d and 16th of the 12th ; and that ift Propofition of the 19th is fupplied by a Lemma in the 12th ...
Seite 2
... Four Sided Figures are fuch as are con- tained under four Lines . XXIII . Many fided Figures are those that are contained under more than four Right Lines . XXIV . Of three fided Figures , that is an XXIV . N Book I. Euclid's ELEMENTS ...
... Four Sided Figures are fuch as are con- tained under four Lines . XXIII . Many fided Figures are those that are contained under more than four Right Lines . XXIV . Of three fided Figures , that is an XXIV . N Book I. Euclid's ELEMENTS ...
Seite 3
... four - fided Figures , that is a Square , whofe four Sides are equal , and its Angles all Right ones . . XXXI . That an Oblong , or Rectangle , which is longer than broad ; but its oppofite fides are equal , and all its Angles Right ...
... four - fided Figures , that is a Square , whofe four Sides are equal , and its Angles all Right ones . . XXXI . That an Oblong , or Rectangle , which is longer than broad ; but its oppofite fides are equal , and all its Angles Right ...
Seite 16
... , make Angles at the Section equal to tour Right Angles . Coroll . 2. All the Angles , conftituted about the fame- Point , are equal to four Right Angles . PRO- PROPOSITION XVI . THEOREM . If one Side of any 16 Euclid's ELEMENTS . Book I.
... , make Angles at the Section equal to tour Right Angles . Coroll . 2. All the Angles , conftituted about the fame- Point , are equal to four Right Angles . PRO- PROPOSITION XVI . THEOREM . If one Side of any 16 Euclid's ELEMENTS . Book I.
Seite xxxii
... four Sides , it may be refolved into two Triangles : If a Figure hath five Sides , it may be refolved into three Triangles ; if fix , into four ; and so on . Wherefore ( by Prop . XXXII . ) the fo Angles of all thefe Triangles are equal ...
... four Sides , it may be refolved into two Triangles : If a Figure hath five Sides , it may be refolved into three Triangles ; if fix , into four ; and so on . Wherefore ( by Prop . XXXII . ) the fo Angles of all thefe Triangles are equal ...
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.