Euclid's Elements of geometry, transl. To which are added, algebraic demonstrations to the second and fifth books; also deductions in the first six, eleventh and twelfth books, with notes, by G. Phillips. Part 1, containing book i-vi1826 |
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Page xxv
... perpendicular . Having thus far exhibited to the reader those votaries of science who flourished in the first period of her history , with their discoveries and improvements , let us turn back to Euclid , the celebrated author of the ...
... perpendicular . Having thus far exhibited to the reader those votaries of science who flourished in the first period of her history , with their discoveries and improvements , let us turn back to Euclid , the celebrated author of the ...
Page 14
... perpendicular right line . Let AB be the given infinite right line , and c a given point which is without it , it is ... perpendicular . Q. E. F. C Deduction . Given the vertex of a triangle , the perpendicular from the vertex to the ...
... perpendicular right line . Let AB be the given infinite right line , and c a given point which is without it , it is ... perpendicular . Q. E. F. C Deduction . Given the vertex of a triangle , the perpendicular from the vertex to the ...
Page 19
... perpendicular is the shortest right line , and that which is nearer to the perpendicular is less than that which is more remote , and there can only be drawn two right lines which are equal to one another , one on each side of the ...
... perpendicular is the shortest right line , and that which is nearer to the perpendicular is less than that which is more remote , and there can only be drawn two right lines which are equal to one another , one on each side of the ...
Page 30
... perpendicular to the base . 3. Given the difference of the angles at the base of a triangle , the perpendicular drawn from the vertex to the base , and one of the segments made by the perpen- dicular , to construct the triangle . 4. To ...
... perpendicular to the base . 3. Given the difference of the angles at the base of a triangle , the perpendicular drawn from the vertex to the base , and one of the segments made by the perpen- dicular , to construct the triangle . 4. To ...
Page 37
... perpendicular the aggregate of the perpendiculars drawn from the vertical angles unto the diagonal . 2. To describe a parallelogram , the area and perimeter of which shall be respectively equal to the area and perimeter of a given ...
... perpendicular the aggregate of the perpendiculars drawn from the vertical angles unto the diagonal . 2. To describe a parallelogram , the area and perimeter of which shall be respectively equal to the area and perimeter of a given ...
Common terms and phrases
ABC is equal adjacent angles Algebra angle ABC angle ACB angle BAC angles equal base BC bisected centre circle ABC circumference diameter double draw equal angles equal circles equal right lines equal to F equi equiangular equimultiples Euclid EUCLID'S ELEMENTS exceed exterior angle fore four magnitudes fourth given circle given point given right line gnomon greater ratio hence inscribed isosceles triangle join less Let ABC multiple parallel parallelogram perpendicular polygon proportional Q. E. D. Deductions Q. E. D. PROPOSITION rectangle contained remaining angle right line AB right line AC right line drawn segment side AC similar and similarly square of AC subtending THEOREM three right lines tiple touches the circle triangle ABC triangle DEF whence whole
Popular passages
Page xxx - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. "A segment of a circle is the figure contained by a straight line, and the circumference it cuts off.
Page 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 33 - The complements of the parallelograms, which are about the diameter of any parallelogram, are equal to one another.
Page 146 - 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.
Page 27 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB, therefore the whole angle ABD is equal to the whole angle ACD • (ax.
Page 2 - 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.
Page 28 - Parallelograms upon the same base, and between the same parallels, are equal to one another.
Page 73 - DH ; (i. def. 15.) therefore DH is greater than DG, the less than the greater, which is impossible : therefore no straight line can be drawn from the point A, between AE and the circumference, which does not cut the circle : or, which amounts to the same thing, however great an acute angle a straight line makes with the diameter at the point A, or however small an angle it makes with AE, the circumference must pass between that straight line and the perpendicular AE.
Page 88 - From a given circle to cut off a segment, which shall contain an angle equal to a given rectilineal angle.
Page 95 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw (1 7. 3.) the straight line G AH touching the circle in the point A, and. at the point A, in the straight line AH, make (23.