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 Plain and Spherical Trigonometry : with a Preface ...T. Woodward, 1723 - 364 σελίδες |
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Σελίδα
... Doctrine of Solids ; and the Properties of Numbers were neceffary to the Reasoning about Incommenfurables : Vide the laft Edition of the English Tacquet . Yet Yet because only one Propofition of these four Books , Mr. Cunn's PREFACE .
... Doctrine of Solids ; and the Properties of Numbers were neceffary to the Reasoning about Incommenfurables : Vide the laft Edition of the English Tacquet . Yet Yet because only one Propofition of these four Books , Mr. Cunn's PREFACE .
Σελίδα
... four Books , viz . the 1ft of the 10th is quo- ted in the 11th and 12th Books ; and that only once , viz . in the Demonstration of the 2d of the 12th , and that 1ft Propofi- tion of the 10th , is fupplied by a Lemma in the 12th : And ...
... four Books , viz . the 1ft of the 10th is quo- ted in the 11th and 12th Books ; and that only once , viz . in the Demonstration of the 2d of the 12th , and that 1ft Propofi- tion of the 10th , is fupplied by a Lemma in the 12th : And ...
Σελίδα 2
... Four - fided Figures , are fuch as are contain❜dun- der four . XXIII . Many fided Figures , are thofe that are contain'd under more than four Right Lines . XXIV . Of three - fided Figures , that is an Equilateral Triangle , which hath ...
... Four - fided Figures , are fuch as are contain❜dun- der four . XXIII . Many fided Figures , are thofe that are contain'd under more than four Right Lines . XXIV . Of three - fided Figures , that is an Equilateral Triangle , which hath ...
Σελίδα 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 , a Figure which is longer on one fide than the other , which is Right- angled , but not equal ...
... Four - fided Figures , that is a Square , whofe four Sides are equal , and its Angles all Right ones . XXXI . That an Oblong , or Rectangle , a Figure which is longer on one fide than the other , which is Right- angled , but not equal ...
Σελίδα 16
... four Right Angles . Coroll . 2. All the Angles conftituted about the fame Point , are equal to four Right Angles . PRO PROPOSITION XVI . THEORE M. If one Side of any 16 Euclid's ELEMENTS . Book I.
... four Right Angles . Coroll . 2. All the Angles conftituted about the fame Point , are equal to four Right Angles . PRO PROPOSITION XVI . THEORE M. If one Side of any 16 Euclid's ELEMENTS . Book I.
Συχνά εμφανιζόμενοι όροι και φράσεις
alfo equal alſo Angle ABC Angle BAC Baſe becauſe bifected Center Circle ABCD Circle EFGH Circumference Cofine Cone confequently contain'd Coroll Cylinder defcrib'd defcribed demonftrated Diameter Diſtance drawn thro equal Angles equiangular equilateral Equimultiples faid fame Altitude fame Multiple fame Plane fame Proportion fame Reafon fecond fhall be equal fimilar fince firft firſt folid Parallelepipedon fome fore ftand fubtending given Right Line Gnomon greater join leffer lefs likewife Logarithm Magnitudes Meaſure Number paffing thro Parallelogram perpendicular Polygon Prifm Priſms Prop PROPOSITION Pyramid Quadrant Ratio Rectangle remaining Angle Right Angles Right Line A B Right Line AB Right-lin'd Figure Right-lin❜d Segment ſhall Sine Solid Sphere Subtangent thefe THEOREM theſe thofe Triangle ABC triplicate Proportion Unity Vertex the Point Wherefore whofe Bafe whole
Δημοφιλή αποσπάσματα
Σελίδα 190 - 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.
Σελίδα 160 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Σελίδα 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Σελίδα 152 - ... therefore the angle DFG is equal to the angle DFE, and the angle at G to the angle at E : but the angle DFG is equal to the angle ACB...
Σελίδα 100 - About a given circle to describe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to describe a triangle about the circle ABC equiangular to the triangle DEF.
Σελίδα 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Σελίδα 210 - CD; therefore AC is a parallelogram. In like manner, it may be proved that each of the figures CE, FG, GB, BF, AE, is a parallelogram...
Σελίδα 229 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Σελίδα 164 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.
Σελίδα 93 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.