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 100
Side 5
... PROPOSITION I. PROBLEM . To defcribe an Equilateral Triangle upon a given finite L Right Line . ET AB be the given finite Right Line , upon which it is required to describe an Equilateral Triangle . About the Center A , with the Di ...
... PROPOSITION I. PROBLEM . To defcribe an Equilateral Triangle upon a given finite L Right Line . ET AB be the given finite Right Line , upon which it is required to describe an Equilateral Triangle . About the Center A , with the Di ...
Side 6
... PROPOSITION III . PROBLEM . Two unequal right Lines being given , to cut off a Part from the greater Equal to the leffer . LE ET AB and C be the two unequal Right Lines gi- ven , the greater whereof is AB ; it is required to cut off a ...
... PROPOSITION III . PROBLEM . Two unequal right Lines being given , to cut off a Part from the greater Equal to the leffer . LE ET AB and C be the two unequal Right Lines gi- ven , the greater whereof is AB ; it is required to cut off a ...
Side 10
... PROPOSITION VII . THEOREM . On the fame Right Line cannot be conftituted two Right Lines equal to two other Right Lines , each to each , at different Points , on the fame Side , and having the fame Ends which the firft Right Lines have ...
... PROPOSITION VII . THEOREM . On the fame Right Line cannot be conftituted two Right Lines equal to two other Right Lines , each to each , at different Points , on the fame Side , and having the fame Ends which the firft Right Lines have ...
Side 11
... PROPOSITION VIII . THEOREM . If two Triangles have two Sides of the one equal to two Sides of the other , each to each , and the Bafes equal , then the Angles contained under the equal Sides will be equal . LET ET the two Triangles be ...
... PROPOSITION VIII . THEOREM . If two Triangles have two Sides of the one equal to two Sides of the other , each to each , and the Bafes equal , then the Angles contained under the equal Sides will be equal . LET ET the two Triangles be ...
Side 12
... PROPOSITION IX . PROBLEM . To cut a given Right - lin❜d Angle into two equal Parts . LE ET BAC be a given Right - lin❜d Angle , which is required to be cut into two equal Parts . Affume any Point D in the Right Line A B , and cut off ...
... PROPOSITION IX . PROBLEM . To cut a given Right - lin❜d Angle into two equal Parts . LE ET BAC be a given Right - lin❜d Angle , which is required to be cut into two equal Parts . Affume any Point D in the Right Line A B , and cut off ...
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.