The Element of GeometryW.E. Dean, 1836 - 114 Seiten |
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Seite 36
... rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC , CB , and to twice ... rectangle contained by AC , CB , for GC is equal to CB ; there- fore GE is ...
... rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC , CB , and to twice ... rectangle contained by AC , CB , for GC is equal to CB ; there- fore GE is ...
Seite 40
... rectangle CF , FA , together with the square of AE , is equal to the squares of BA , AE : take away the square of AE ... twice the rectangle contained by the whole and that part , together with the square of the other part . Let the ...
... rectangle CF , FA , together with the square of AE , is equal to the squares of BA , AE : take away the square of AE ... twice the rectangle contained by the whole and that part , together with the square of the other part . Let the ...
Seite 41
... twice the rectangle contained by the side upon which when produced the perpendicular falls , and the straight line intercepted without the triangle between the perpendicular and the obtuse angle . Let ABC be an obtuse angled triangle ...
... twice the rectangle contained by the side upon which when produced the perpendicular falls , and the straight line intercepted without the triangle between the perpendicular and the obtuse angle . Let ABC be an obtuse angled triangle ...
Seite 42
... twice the rectangle contained by CB , BD , and the square of DC : to each of these equals add the square of AD ; therefore the squares of CB , BD , ᎠᎪ are equal to twice the rectangle CB BD , and the squares of AD , DC : but the ...
... twice the rectangle contained by CB , BD , and the square of DC : to each of these equals add the square of AD ; therefore the squares of CB , BD , ᎠᎪ are equal to twice the rectangle CB BD , and the squares of AD , DC : but the ...
Seite 108
... triangle , & c . Q. E. D. In PROP . V. any triangle , twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides , and the square of the base , as the radius is to the co - sine of ...
... triangle , & c . Q. E. D. In PROP . V. any triangle , twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides , and the square of the base , as the radius is to the co - sine of ...
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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...