A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 93
... half the line and of the square on the line between the points of section . Let the straight line AB be divided into two 1 . equal parts at the point C , and into two un- equal parts at the point D : the squares on AD , DB shall be ...
... half the line and of the square on the line between the points of section . Let the straight line AB be divided into two 1 . equal parts at the point C , and into two un- equal parts at the point D : the squares on AD , DB shall be ...
Página 94
... half a right angle . For the same reason each of the angles CEB , EBC is half a right angle . Therefore the whole angle AEB is a right angle . And because the angle GEF is half a right angle , and the angle EGF a right angle , for it is ...
... half a right angle . For the same reason each of the angles CEB , EBC is half a right angle . Therefore the whole angle AEB is a right angle . And because the angle GEF is half a right angle , and the angle EGF a right angle , for it is ...
Página 95
... half the line bisected and of the square on the line made up of the half and the part produced . Let the straight line AB be bisected at C , and 1 . produced to D : the squares on AD , DB shall be together double of the squares on AC ...
... half the line bisected and of the square on the line made up of the half and the part produced . Let the straight line AB be bisected at C , and 1 . produced to D : the squares on AD , DB shall be together double of the squares on AC ...
Página 96
... half a right angle , the angle DBC is also half a right angle , for they are vertically opposite ; [ I. 15. ] but the angle BDG is a right angle , because it is equal to the alternate angle DCE ; [ I. 29. ] therefore the remaining angle ...
... half a right angle , the angle DBC is also half a right angle , for they are vertically opposite ; [ I. 15. ] but the angle BDG is a right angle , because it is equal to the alternate angle DCE ; [ I. 29. ] therefore the remaining angle ...
Página 105
... half the quadrilateral , therefore D A B : AECB = OECB . Take away the common part ABC , then the triangle AEC is equal to the triangle 40C ; and they are on the same base , therefore they are between the same parallels and EO is ...
... half the quadrilateral , therefore D A B : AECB = OECB . Take away the common part ABC , then the triangle AEC is equal to the triangle 40C ; and they are on the same base , therefore they are between the same parallels and EO is ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle DBA angle EDF angle equal angles are equal axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid EUCLID'S ELEMENTS exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal
Pasajes populares
Página 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Página 28 - If two triangles have two sides of the one equal to two sides of the...
Página 41 - Any two sides of a triangle are together greater than the third side.
Página 57 - 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 72 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Página 75 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 89 - 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...
Página 55 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Página 28 - A two triangles, having the two sides AB, AC, equal to the two sides \ DE, DF, each to each, viz: AB to DE, and AC to DF; and also the base BC equal to the base EF.
Página 69 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.