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 páginas |
Dentro del libro
Resultados 1-5 de 42
Página 4
... double to one and the fame Thing , are equal between themselves . VII . Things , which are half one and the fame Thing , are equal between themselves . VIII . Things which mutually agree together , are equal to one another . IX . The ...
... double to one and the fame Thing , are equal between themselves . VII . Things , which are half one and the fame Thing , are equal between themselves . VIII . Things which mutually agree together , are equal to one another . IX . The ...
Página 38
... double the Tri- angle ABC , fince the Diameter AC bifects it . Where- fore likewife it fhall be double to the Triangle EBC . If , therefore , a Parallelogram and Triangle have both the fame Bafe , and are between the fame Parallels ...
... double the Tri- angle ABC , fince the Diameter AC bifects it . Where- fore likewife it fhall be double to the Triangle EBC . If , therefore , a Parallelogram and Triangle have both the fame Bafe , and are between the fame Parallels ...
Página 39
... double to the Triangle A EC . But the Parallelogram F ECG is alfo double to the Triangle A EC ; for it has the fame Bafe , and is between the fame Parallels . There- fore the Parallelogram FECG , is equal to the Tri- angle ABC , and has ...
... double to the Triangle A EC . But the Parallelogram F ECG is alfo double to the Triangle A EC ; for it has the fame Bafe , and is between the fame Parallels . There- fore the Parallelogram FECG , is equal to the Tri- angle ABC , and has ...
Página 42
... double to the Triangle ABD ; for they have the fame Base DB , and are between the fame Parallels BD , AL . The Square GB is alfo double to the Triangle FBC ; for they have the fame Bafe FB , and are in the fame Parallels FB , GC . But ...
... double to the Triangle ABD ; for they have the fame Base DB , and are between the fame Parallels BD , AL . The Square GB is alfo double to the Triangle FBC ; for they have the fame Bafe FB , and are in the fame Parallels FB , GC . But ...
Página 52
... double the Rectangle contain'd under the whole Line , and the faid Segment , together with the Square , made of the other Segment . LET the Right Line A B be any how cut in the Point C. I fay the Squares of AB , BC , toge ther , are ...
... double the Rectangle contain'd under the whole Line , and the faid Segment , together with the Square , made of the other Segment . LET the Right Line A B be any how cut in the Point C. I fay the Squares of AB , BC , toge ther , are ...
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 63 - DBA ; and because AE, a side of the triangle DAE, is produced to B, the angle DEB is greater (16.
Página 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...
Página 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.
Página 17 - CF, and the triangle AEB to the triangle CEF, and the remaining angles to the remaining angles, each to each, to which...
Página 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...
Página 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.
Página 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.
Página 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.