The elements of plane geometry; or, The first six books of Euclid, ed. by W. Davis1863 |
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Αποτελέσματα 6 - 10 από τα 13.
Σελίδα 48
... perpendicular to the line touching the circle . For , if FC be not perpendicular to DE ; from the point F draw FG perpendicular to DE , and let it meet the circumference in B. Because FGC is a right angle , GCF is an acute angle ( I. 17 ) ...
... perpendicular to the line touching the circle . For , if FC be not perpendicular to DE ; from the point F draw FG perpendicular to DE , and let it meet the circumference in B. Because FGC is a right angle , GCF is an acute angle ( I. 17 ) ...
Σελίδα 56
... perpendicular ( I. 12 ) to AC . D E G B Because AG is equal ( III . 3 ) , to GC , the rectangle A E. EC , toge- ther with the square of EG , is equal ( II . 5 ) to the square of AG . To each of these equals add the square of GF ...
... perpendicular ( I. 12 ) to AC . D E G B Because AG is equal ( III . 3 ) , to GC , the rectangle A E. EC , toge- ther with the square of EG , is equal ( II . 5 ) to the square of AG . To each of these equals add the square of GF ...
Σελίδα 57
... perpendicular to AC ( I. 12 ) and join EB , EC , and ED . F Because the straight line EF , passing through the centre , cuts the straight line AC , which does not pass through the centre , at right angles , it bisects AC ( III . 3 ) ...
... perpendicular to AC ( I. 12 ) and join EB , EC , and ED . F Because the straight line EF , passing through the centre , cuts the straight line AC , which does not pass through the centre , at right angles , it bisects AC ( III . 3 ) ...
Σελίδα 87
... perpendicular to the base . Д PROP . I. ( THEOREM ) -Triangles ( ABC and ACD ) and parallelograms ( EC and CF ) of the same altitude are to one another as their bases . Produce BD both ways to the points H and L , and take any number of ...
... perpendicular to the base . Д PROP . I. ( THEOREM ) -Triangles ( ABC and ACD ) and parallelograms ( EC and CF ) of the same altitude are to one another as their bases . Produce BD both ways to the points H and L , and take any number of ...
Σελίδα 88
... perpendicular drawn from the point E to AB , and they are to one another as their bases . For the same reason , the triangle CDE is to the triangle ADE as CE to EA . Therefore , as BD is to DA so is CE to EA ( V. 11 ) . Next , let the ...
... perpendicular drawn from the point E to AB , and they are to one another as their bases . For the same reason , the triangle CDE is to the triangle ADE as CE to EA . Therefore , as BD is to DA so is CE to EA ( V. 11 ) . Next , let the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD adjacent angles alternate angle angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF arc BC base BC bisected centre circle ABC circumference double equal angles equal Ax equal Const equal Hyp equal to F equals add equiangular equimultiples exterior angle four magnitudes fourth G and H given straight line gnomon greater ratio greater than F interior and opposite join less multiple opposite angle parallel parallelogram parallelogram BD perpendicular PROBLEM.)-To produced Q. E. D. PROP rectangle contained remaining angle right angles segment side BC square of AC straight line AB straight line AC THEOREM.)-If three straight lines touches the circle triangle ABC triangle DEF twice the rectangle whole angle
Δημοφιλή αποσπάσματα
Σελίδα 3 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VIII. A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.
Σελίδα 4 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Σελίδα 67 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Σελίδα 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 93 - From this it is manifest, that the perpendicular drawn from the right angle of a right-angled triangle to the base, is a mean proportional between the segments of the base; and also that each of the sides is a mean proportional between the base, and...
Σελίδα 68 - This word is used when there are four proportionals, and it is inferred that the first has the same ratio to the third which the second has to the fourth ; or that the first is to the third as the second to the fourth : as is shown in Prop.
Σελίδα 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 88 - From this it is plain, that triangles and parallelograms that have equal altitudes, are to one another as their bases. Let the figures be placed so as to have their bases in the same straight line; and having drawn perpendiculars from the vertices of the triangles to the bases, the straight line which joins the vertices is parallel to that in which their bases are, (I.
Σελίδα 69 - This term is used when the first magnitude is to the second of the first rank, as the last but one is to the last of the second rank; and as the second is to the third of the first rank, so is the last but two to the last but one of the second rank; and as the third is to the fourth of the first rank, so is the third from the last to the last but two of the second rank; and so on in a cross order: and the inference is as in the 18th definition.
Σελίδα 21 - ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.