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 sider |
Inni boken
Resultat 1-5 av 46
Side 1
... touch each other , but do not both lie in the fame Right Line . IX . If the Lines containing the Angle be Right ones , then the Angle is called a Right - lin❜d Angle . X. When B g X. When a RightLine , standing on another Right ( x )
... touch each other , but do not both lie in the fame Right Line . IX . If the Lines containing the Angle be Right ones , then the Angle is called a Right - lin❜d Angle . X. When B g X. When a RightLine , standing on another Right ( x )
Side 63
... touch a Cir cle , when touching the same , and being produc'd , does not cut it . III . Circles are faid to touch each other , which Touching do not cut one another . IV . Right Lines in a Circle are faid to be equally dif tant from the ...
... touch a Cir cle , when touching the same , and being produc'd , does not cut it . III . Circles are faid to touch each other , which Touching do not cut one another . IV . Right Lines in a Circle are faid to be equally dif tant from the ...
Side 66
... touch it in one Point only . PROPOSITION . III . THEOREM . If in a Circle a Right Line drawn through the Center , cuts any other Right Line not drawn through the Center , into equal Parts , it shall cut it at Right An- gles ; and if it ...
... touch it in one Point only . PROPOSITION . III . THEOREM . If in a Circle a Right Line drawn through the Center , cuts any other Right Line not drawn through the Center , into equal Parts , it shall cut it at Right An- gles ; and if it ...
Side 68
... touch one another inwardly , they will not have one and the fame Center . LE ET two Circles ABC , CDE , touch one another inwardly in the Point C. I fay , they will not have one and the fame Center . For if they have , let it be F , and ...
... touch one another inwardly , they will not have one and the fame Center . LE ET two Circles ABC , CDE , touch one another inwardly in the Point C. I fay , they will not have one and the fame Center . For if they have , let it be F , and ...
Side 74
... - ting each other , which is abfurd . Wherefore a Cir- cle cannot cut a Circle in more than two Points ; which was to be demonftrated . PRO PROPOSITION XI . THEOREM . If two Circles touch each 74 Euclid's ELEMENTS . Book III .
... - ting each other , which is abfurd . Wherefore a Cir- cle cannot cut a Circle in more than two Points ; which was to be demonftrated . PRO PROPOSITION XI . THEOREM . If two Circles touch each 74 Euclid's ELEMENTS . Book III .
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Side 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...
Side 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.
Side 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Side 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...
Side 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.
Side 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.
Side 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.