The Element of GeometryW.E. Dean, 1836 - 114 páginas |
Dentro del libro
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Página 35
... square of AC ; there- fore the squares of AD , AC are equal to the squares of AB , AC ; but the square of CD is equal ( 17. 2. ) to the squares of AD , AC , be- cause DAC is a right angle ; and the square of BC , by hypothesis , is equal to ...
... square of AC ; there- fore the squares of AD , AC are equal to the squares of AB , AC ; but the square of CD is equal ( 17. 2. ) to the squares of AD , AC , be- cause DAC is a right angle ; and the square of BC , by hypothesis , is equal to ...
Página 36
... square of the whole line is equal to the squares of the two parts , together with twice the 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 ...
... square of the whole line is equal to the squares of the two parts , together with twice the 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 ...
Página 39
... square of EC is equal to the square of CA ; therefore the squares of EC , CA are double of the square of CA : but the square of EA is equal ( 17.2 . ) to the squares of EC , CA ; there- fore the square of EA is double of the square of AC ...
... square of EC is equal to the square of CA ; therefore the squares of EC , CA are double of the square of CA : but the square of EA is equal ( 17.2 . ) to the squares of EC , CA ; there- fore the square of EA is double of the square of AC ...
Página 40
John Playfair. AE , is equal to the square of EB : and the squares of BA , AE are equal ( 17. 2. ) to the square of ... AC . Upon AB describe ( 16. 2. ) the square ADEB , and construct the figure as in the preceding propositions ...
John Playfair. AE , is equal to the square of EB : and the squares of BA , AE are equal ( 17. 2. ) to the square of ... AC . Upon AB describe ( 16. 2. ) the square ADEB , and construct the figure as in the preceding propositions ...
Página 41
... square of AB is greater than the squares of AC , CB by twice the rectangle BC , CD . Because the straight line BD is divided into two parts in the point C , the square of BD is equal ( 20. 2. ) to the squares of BC , CD , and twice the ...
... square of AB is greater than the squares of AC , CB by twice the rectangle BC , CD . Because the straight line BD is divided into two parts in the point C , the square of BD is equal ( 20. 2. ) to the squares of BC , CD , and twice the ...
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...