A Text-book of Geometrical Deductions: Book I [-II] Corresponding to Euclid, Book I [-II], Book 2Longmans, Green and Company, 1892 - Geometry |
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Page 141
... 99 " " II . Theorems , 99 " " Problems , DEFINITIONS . Segments , Point of Internal Section , Point of External Section , Medial Section , Orthogonal Projection , 184 192 197 199 145 • 152 159 166 - :: - || |||| Δ L SYMBOLS . signifies.
... 99 " " II . Theorems , 99 " " Problems , DEFINITIONS . Segments , Point of Internal Section , Point of External Section , Medial Section , Orthogonal Projection , 184 192 197 199 145 • 152 159 166 - :: - || |||| Δ L SYMBOLS . signifies.
Page 166
... Projection of one straight line on another is the part of the latter intercepted between perpendiculars let fall on ... projection of AB on CD . It is clear that the length LM depends only on the length of AB and the angle which AB makes ...
... Projection of one straight line on another is the part of the latter intercepted between perpendiculars let fall on ... projection of AB on CD . It is clear that the length LM depends only on the length of AB and the angle which AB makes ...
Page 167
... projection of BO on AO . The theorem may , therefore , be stated thus : - If there be two straight lines , the rectangle contained by the first and the projection on it of the second is equal to the rectangle contained by the second and ...
... projection of BO on AO . The theorem may , therefore , be stated thus : - If there be two straight lines , the rectangle contained by the first and the projection on it of the second is equal to the rectangle contained by the second and ...
Page 168
... projection on it of the other side ( Euc . II . 12 ) . R S E B K In figure 1 , construct squares as in Euclid I. 47 , and draw BRP , CSQL AC , AB . As in Euc . I. 47 , show that BL = FS = AF + AQ = AB2 + BA.AS ; and similarly , that CL ...
... projection on it of the other side ( Euc . II . 12 ) . R S E B K In figure 1 , construct squares as in Euclid I. 47 , and draw BRP , CSQL AC , AB . As in Euc . I. 47 , show that BL = FS = AF + AQ = AB2 + BA.AS ; and similarly , that CL ...
Page 169
... projection on it of the other side ( Euc . II . 13 ) . R H D E B The constructions are similar to those of the previous Ex . In figure 1 , show that BL = FS = AB2 — AB.AS , etc. Otherwise- In figure 2 , AHFBC + GHKCD = GHFBCD + AHKC ...
... projection on it of the other side ( Euc . II . 13 ) . R H D E B The constructions are similar to those of the previous Ex . In figure 1 , show that BL = FS = AB2 — AB.AS , etc. Otherwise- In figure 2 , AHFBC + GHKCD = GHFBCD + AHKC ...
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A Text-Book of Geometrical Deductions: Book I [-II] Corresponding to Euclid ... William Thomson No preview available - 2016 |
Common terms and phrases
AB=AC AB=BC altitude angle is equal Apply Euc Apply Ex base BC BC is trisected BC meets BC produced bisector Bookwork Construct a rectangle Construct a triangle difference distances divided externally equal to twice EUCLID exterior angle figure find a point find the locus four points geometrical construction given points given square given straight line given the base half the line internally at H isosceles triangle James Thin joining the mid-points line be divided line be drawn lines is equal medial section medians meet AC mid-point of AB mid-points of BC obtuse angle parallel straight lines parallelogram perimeter perpendicular drawn point in AB point in BC point of intersection points in order previous Ex rectangle ABCD rectangle contained rectangle equal rhombus right-angled triangle segments square on half Standard Theorem trapezium twice the rectangle twice the square vertex whole line
Popular passages
Page 180 - 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 of the line between the points of section, is equal to the square of half the line.
Page 181 - 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.
Page 181 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 180 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Page 169 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Page 181 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Page 181 - 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...
Page 168 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 171 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Page 162 - In any triangle the sum of the squares on two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side.