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
... greater ; but fometimes one lefs , and the other greater , as in the two laft mention'd Cafes . When it is not doubtful , the Quæfitum is fometimes greater than 90 Degrees , and and fometimes lefs . All which Diftinctions may be made ...
... greater ; but fometimes one lefs , and the other greater , as in the two laft mention'd Cafes . When it is not doubtful , the Quæfitum is fometimes greater than 90 Degrees , and and fometimes lefs . All which Diftinctions may be made ...
Σελίδα 6
... greater whereof is AB ; it is required to cut off a Line from the greater AB equal to the leffer C. Put a right Line AD at the Point A , equal to the Line C , and about the Center A , with the Distance AD , defcribe a Circle DEFt . Then ...
... greater whereof is AB ; it is required to cut off a Line from the greater AB equal to the leffer C. Put a right Line AD at the Point A , equal to the Line C , and about the Center A , with the Distance AD , defcribe a Circle DEFt . Then ...
Σελίδα 10
... greater than the Angle BCD ; wherefore the Angle BDC will be much greater than the Angle B CD . Again , because C B is equal to DB , the Angle BDC will be equal to the Angle B CD ; but it has been proved to be much greater , which is ...
... greater than the Angle BCD ; wherefore the Angle BDC will be much greater than the Angle B CD . Again , because C B is equal to DB , the Angle BDC will be equal to the Angle B CD ; but it has been proved to be much greater , which is ...
Σελίδα 17
... greater than the Angle ECF ; therefore the Angle ACD , is greater than the Angle BAE . After the fame manner , if the Right Line BC , be bifected , we demonftrate that the Angle BCG , that is , the Angle ACD , is greater than the Angle ...
... greater than the Angle ECF ; therefore the Angle ACD , is greater than the Angle BAE . After the fame manner , if the Right Line BC , be bifected , we demonftrate that the Angle BCG , that is , the Angle ACD , is greater than the Angle ...
Σελίδα 18
... greater Side of every Triangle fubtends the greater LE Angle . ET ABC be a Triangle , having the Side AC greater than the Side AB . I fay the Angle ABC is greater than the Angle BCA . For because AC is greater than AB , AD may be made ...
... greater Side of every Triangle fubtends the greater LE Angle . ET ABC be a Triangle , having the Side AC greater than the Side AB . I fay the Angle ABC is greater than the Angle BCA . For because AC is greater than AB , AD may be made ...
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.