The Element of GeometryW.E. Dean, 1836 - 114 Seiten |
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Seite 84
... duplicate ratio of their homologous sides . Let ABC , DEF be similar triangles having the angle B equal to the angle E , and let AB be to BC , as DE to EF , so that the side BC is homologous to EF ( Def . 10. 5. ) ; the triangle ABC has ...
... duplicate ratio of their homologous sides . Let ABC , DEF be similar triangles having the angle B equal to the angle E , and let AB be to BC , as DE to EF , so that the side BC is homologous to EF ( Def . 10. 5. ) ; the triangle ABC has ...
Seite 85
... duplicate ratio of that which it has to the second ; BC therefore has to BG the duplicate ratio of that which BC has to EF : but as BC to BG , so is ( 2. Cor . 2. 5. ) the triangle ABC to the triangle ABG . Therefore the triangle ABC ...
... duplicate ratio of that which it has to the second ; BC therefore has to BG the duplicate ratio of that which BC has to EF : but as BC to BG , so is ( 2. Cor . 2. 5. ) the triangle ABC to the triangle ABG . Therefore the triangle ABC ...
Seite 86
... duplicate ratio of that which the side AB has to the homologous side FG . Because the triangle ABE is similar to the triangle FGL , ABE has to FGL the duplicate ratio ( 19. 5. ) of that which the side BE has to the side GL ; for the ...
... duplicate ratio of that which the side AB has to the homologous side FG . Because the triangle ABE is similar to the triangle FGL , ABE has to FGL the duplicate ratio ( 19. 5. ) of that which the side BE has to the side GL ; for the ...
Seite 87
... duplicate ratio of their homologous sides , and it has already been proved in tri- angles . Therefore universally , similar rectilineal figures are to one another in the duplicate ratio of their homologous sides . COR . 2. And if to AB ...
... duplicate ratio of their homologous sides , and it has already been proved in tri- angles . Therefore universally , similar rectilineal figures are to one another in the duplicate ratio of their homologous sides . COR . 2. And if to AB ...
Seite 98
... duplicate ratio of BA to GF but the ratio of the square of BM to the square of GN , is the duplicate ( 20. 5. ) ratio of that which BM has to GN ; and the ratio of the polygon ABCDE to the polygon FGHKL , is the duplicate ratio of that ...
... duplicate ratio of BA to GF but the ratio of the square of BM to the square of GN , is the duplicate ( 20. 5. ) ratio of that which BM has to GN ; and the ratio of the polygon ABCDE to the polygon FGHKL , is the duplicate ratio of that ...
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The Element of Geometry (Classic Reprint) Formerly Chairman Department of Immunology John Playfair,John Playfair Keine Leseprobe verfügbar - 2017 |
Häufige Begriffe und Wortgruppen
AB is equal AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF arc AC base BC bisect called centre circle ABCD circle EFGH coincide described divided drawn duplicate ratio equal 17 equal angles equal circles equal to CD equiangular FGHKL fore four right angles given straight line gnomon greater homologous sides join less Let ABC Let the straight opposite angles parallel parallelogram perpendicular polygon PROB produced Q. E. D. PROP radius rectangle BC rectangle contained rectilineal figure remaining angle right angled triangle secant segment side AC similar sine square of AC straight line AB straight line AC THEOR touches the circle triangle ABC twice the rectangle wherefore whole angle
Beliebte Passagen
Seite 25 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Seite 13 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line E iR.
Seite 4 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Seite 29 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Seite 90 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Seite 87 - ... magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Seite 1 - If two triangles have two sides of the one equal to two sides of the...
Seite 13 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Seite 64 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 19 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...