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 143
... means of a Geometrical Con- struction . K B M C E Draw CE and DGLAD and equal to BD and BC respec- tively . Complete the rectangles AG , AE and AM . Prove that CG and KE are rectangles contained by equal lines , and are therefore equal ...
... means of a Geometrical Con- struction . K B M C E Draw CE and DGLAD and equal to BD and BC respec- tively . Complete the rectangles AG , AE and AM . Prove that CG and KE are rectangles contained by equal lines , and are therefore equal ...
Page 145
... . Similarly AC2 = BC⚫NC . 2. Prove the above theorem by means of the geometrical construction employed by Euclid in proving Euc . I. 47 . K 3. In any triangle in which the altitude from the § 32. ] 145 Book II .-- Theorems 32 99 1-
... . Similarly AC2 = BC⚫NC . 2. Prove the above theorem by means of the geometrical construction employed by Euclid in proving Euc . I. 47 . K 3. In any triangle in which the altitude from the § 32. ] 145 Book II .-- Theorems 32 99 1-
Page 146
... means of Euc . I. 47 , II . 4 , and by the method of the previous Ex . 6. ABCD is a square , and through P a point in AB , PQR is drawn AB , meeting AC in Q , and DC in R ; show that AP PB = PQ QR = AQ QC . B D R Apply Euc . II . 4 to ...
... means of Euc . I. 47 , II . 4 , and by the method of the previous Ex . 6. ABCD is a square , and through P a point in AB , PQR is drawn AB , meeting AC in Q , and DC in R ; show that AP PB = PQ QR = AQ QC . B D R Apply Euc . II . 4 to ...
Page 148
... means of a geometrical construction similar to that used in Euc . II . 4 . 16. A , B , C , D are four points in order in a straight line , and BC = CD ; show that AB2 + 2AC CD = AC2 + CD2 . 17. A , B , C , D , E are five points in order ...
... means of a geometrical construction similar to that used in Euc . II . 4 . 16. A , B , C , D are four points in order in a straight line , and BC = CD ; show that AB2 + 2AC CD = AC2 + CD2 . 17. A , B , C , D , E are five points in order ...
Page 149
... means of a geometrical con- struction . E K A C B Let AB , AC be the given straight lines . Describe squares on them as in the figure , and produce ED to K , so that AC . Produce GF and draw KLIGF . DK Prove EL EH + FB , etc. Observe ...
... means of a geometrical con- struction . E K A C B Let AB , AC be the given straight lines . Describe squares on them as in the figure , and produce ED to K , so that AC . Produce GF and draw KLIGF . DK Prove EL EH + FB , etc. Observe ...
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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.