Elements of geometry, based on Euclid, books i-iii1876 - 119 páginas |
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Página 56
... twice the side of a square equal to the rectangle contained by these lines , the triangle shall be right - angled ... rectangle contained by one of the perpendiculars and the perimeter of the triangle is double the area of the triangle ...
... twice the side of a square equal to the rectangle contained by these lines , the triangle shall be right - angled ... rectangle contained by one of the perpendiculars and the perimeter of the triangle is double the area of the triangle ...
Página 61
... square on the whole line is equal to the sum of the squares on 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 on AB shall be equal to ...
... square on the whole line is equal to the sum of the squares on 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 on AB shall be equal to ...
Página 72
... rectangle CF , FA , together with the square on AE , is equal to the squares on AE and AB . Take away the square on ... twice the rectangle contained by the side on which , when produced , the perpendicular falls , and the straight line ...
... rectangle CF , FA , together with the square on AE , is equal to the squares on AE and AB . Take away the square on ... twice the rectangle contained by the side on which , when produced , the perpendicular falls , and the straight line ...
Página 73
... twice the rectangle BC , CD . = BC2 + But the square on BA is equal to the squares on BD and ( CD2 + DA , because ... twice the rectangle BC , CD ; that is , the square on BA is greater than the squares on BC and CA by twice the ...
... twice the rectangle BC , CD . = BC2 + But the square on BA is equal to the squares on BD and ( CD2 + DA , because ... twice the rectangle BC , CD ; that is , the square on BA is greater than the squares on BC and CA by twice the ...
Página 74
... twice the rectangle CB , BD ; that is , the square on AC alone is less than the squares on CB and BA by twice the rectangle CB , BD . Б CASE II . - Secondly , let AD fall without the triangle ABC . PROOF . Because the angle at D is a ...
... twice the rectangle CB , BD ; that is , the square on AC alone is less than the squares on CB and BA by twice the rectangle CB , BD . Б CASE II . - Secondly , let AD fall without the triangle ABC . PROOF . Because the angle at D is a ...
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Términos y frases comunes
ABCD angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect centre chord circle ABC circumference coincide common Const CONSTRUCTION describe diagonal diameter difference divided double draw drawn equal to CD exterior angle extremities fall figure four given point given rectilineal given straight line gnomon greater impossible join length less Let ABC Let the straight manner meet opposite angles parallel parallelogram pass perpendicular possible produced PROOF PROOF.-Because proved Q. E. D. Proposition rectangle contained right angles segment semicircle shown side BC sides square on AC Take taken third touches the circle triangle ABC twice the rectangle unequal
Pasajes populares
Página 37 - 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 equal to two right angles.
Página 13 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC be produced to D and E.
Página 7 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 17 - If two triangles have two sides of the one equal to two sides of the...
Página 53 - If the square described upon one of the sides of a triangle, be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle.
Página 9 - 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...
Página 71 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 9 - Things which are double of the same, are equal to one another. 7. Things which are halves of the same, are equal to one another.
Página 34 - Wherefore, if a straight line, &c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line ; or make the interior angles upon the same side together equal to two right angles ; the two straight lines shall be parallel to one another.
Página 69 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line, which is made up of the half and the part produced.