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 2
... Segment of a Circle , is a Figure contain'd un- der a Right Line , and Part of the Circumference of the Circle [ which is cut off by that Right Line . ] XX . Right - lin'dFigures , are fuch as are contain'd under Right Lines . XXI ...
... Segment of a Circle , is a Figure contain'd un- der a Right Line , and Part of the Circumference of the Circle [ which is cut off by that Right Line . ] XX . Right - lin'dFigures , are fuch as are contain'd under Right Lines . XXI ...
Σελίδα 46
... Segments of the divided Line : ET A and BC be two Right Lines , whereof BC is cut or divided any how in the Points D , E. I fay , the Rectangle contamed under the Right Lines A and BC , is equal to the Rectangles contained under A and ...
... Segments of the divided Line : ET A and BC be two Right Lines , whereof BC is cut or divided any how in the Points D , E. I fay , the Rectangle contamed under the Right Lines A and BC , is equal to the Rectangles contained under A and ...
Σελίδα 47
... Segments , or Parts , are equal to the Square of the whole Line . PROPOSITION III . THEOREM . If a Right Line be any how cut , the Rectangle con- tained under the whole Line , and one of its Parts , is equal to the Rectangle contained ...
... Segments , or Parts , are equal to the Square of the whole Line . PROPOSITION III . THEOREM . If a Right Line be any how cut , the Rectangle con- tained under the whole Line , and one of its Parts , is equal to the Rectangle contained ...
Σελίδα 48
... Segments thereof , together with twice the Rectangle contained under the Segments . TET the Right Line AB be any how cut in C. I fay , the Square made on A B is equal to the Squares of AC , CB , together , with twice the Rect- angle ...
... Segments thereof , together with twice the Rectangle contained under the Segments . TET the Right Line AB be any how cut in C. I fay , the Square made on A B is equal to the Squares of AC , CB , together , with twice the Rect- angle ...
Σελίδα 49
... Segments thereof , together with twice the Rectangle contained under the Segments ; which was to be demonftrated . Coroll . Hence it is manifeft , that the Parallelograms which ftand about the Diameter of a Square , are likewife Squares ...
... Segments thereof , together with twice the Rectangle contained under the Segments ; which was to be demonftrated . Coroll . Hence it is manifeft , that the Parallelograms which ftand about the Diameter of a Square , are likewife Squares ...
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.