The Element of GeometryW.E. Dean, 1836 - 114 páginas |
Dentro del libro
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Página 19
... less than ACF ( Def . 16. ) ; and therefore AB , the half of AF , is less than AC , the half of ACF ; therefore the perpendicular is shorter than any oblique . Because the triangles ABC , ABE have the side BC equal to the side BE , the ...
... less than ACF ( Def . 16. ) ; and therefore AB , the half of AF , is less than AC , the half of ACF ; therefore the perpendicular is shorter than any oblique . Because the triangles ABC , ABE have the side BC equal to the side BE , the ...
Página 31
... less than two right an- gles , these straight lines being continually produced , shall at - length meet upon that side on which are the angles , which are less than two right angles . Let the straight line AC fall on the straight lines ...
... less than two right an- gles , these straight lines being continually produced , shall at - length meet upon that side on which are the angles , which are less than two right angles . Let the straight line AC fall on the straight lines ...
Página 46
... less , which is impossible ; there- fore G is not the centre of the circle ABC . In the same manner it can be shewn ... less than DA . 0 Because DF is nearer the perpen- dicular DE , it is less than DA ( 13 . 1. ) : in the same way ...
... less , which is impossible ; there- fore G is not the centre of the circle ABC . In the same manner it can be shewn ... less than DA . 0 Because DF is nearer the perpen- dicular DE , it is less than DA ( 13 . 1. ) : in the same way ...
Página 49
... less than the square of EK , because EH is less than EK ; therefore the square of BH is greater than the square of FK , and the straight line BH greater than FK ; and therefore BC is greater than FG . Next , Let BC be greater than FG ...
... less than the square of EK , because EH is less than EK ; therefore the square of BH is greater than the square of FK , and the straight line BH greater than FK ; and therefore BC is greater than FG . Next , Let BC be greater than FG ...
Página 56
... less to the less . Let ABC , DEF be equal circles , and BC , EF equal straight lines in them , which cut off the two greater circumferences BAC , EDF , and the two less BGC , EHF ; the greater BAC is equal to the greater EDF , and ...
... less to the less . Let ABC , DEF be equal circles , and BC , EF equal straight lines in them , which cut off the two greater circumferences BAC , EDF , and the two less BGC , EHF ; the greater BAC is equal to the greater EDF , and ...
Otras ediciones - Ver todas
The Element of Geometry (Classic Reprint) Formerly Chairman Department of Immunology John Playfair,John Playfair Sin vista previa disponible - 2017 |
Términos y frases comunes
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 angles equal circles equal to AC equiangular FGHKL fore four right angles given straight line gnomon greater homologous sides interior angles 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
Pasajes populares
Página 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.
Página 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.
Página 4 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Página 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...
Página 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.
Página 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.
Página 1 - If two triangles have two sides of the one equal to two sides of the...
Página 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.
Página 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.
Página 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...