The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |
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Αποτελέσματα 1 - 5 από τα 16.
Σελίδα 40
IN any right angled triangle , the square which is described upon the side
fubtending the right angle , is equal to the squares described upon the sides
which contain the right angle . Let ABC be a right angled triangle having the right
angle ...
IN any right angled triangle , the square which is described upon the side
fubtending the right angle , is equal to the squares described upon the sides
which contain the right angle . Let ABC be a right angled triangle having the right
angle ...
Σελίδα 101
... GH , GK are equal to one another ; and the circle described from the center G ,
at the distance of one of them B H H C shall pass thro'the extremities of the other
three , and touch the straight lines AB , BC , CD , DA ; because the angles at the ...
... GH , GK are equal to one another ; and the circle described from the center G ,
at the distance of one of them B H H C shall pass thro'the extremities of the other
three , and touch the straight lines AB , BC , CD , DA ; because the angles at the ...
Σελίδα 103
... to the angies CDA , DAC ; therefore also BCD is double of DAC . and BCD is
equal to each of the angles BDA , DBA ; each therefore of the angles BDA , DBA
is double of the angle DAB . wherefore an isosceles triangle ABD is described ...
... to the angies CDA , DAC ; therefore also BCD is double of DAC . and BCD is
equal to each of the angles BDA , DBA ; each therefore of the angles BDA , DBA
is double of the angle DAB . wherefore an isosceles triangle ABD is described ...
Σελίδα 167
... sides about the equal angles proportionals , they are similar to che another .
and in the same manner a rectilineal figure of six fides may be described upon a
given straight line similar to one given , and so on . Which was to be done , PROP
.
... sides about the equal angles proportionals , they are similar to che another .
and in the same manner a rectilineal figure of six fides may be described upon a
given straight line similar to one given , and so on . Which was to be done , PROP
.
Σελίδα 176
E. D. d . 9.5 • To understand the three following propofitions more eally , it is to be
observed , 1. That a parallelogram is said to be applied to a straight line , when it
is described upon it as one of its sides . Ex . gr . the pa• rallelogram AC is said ...
E. D. d . 9.5 • To understand the three following propofitions more eally , it is to be
observed , 1. That a parallelogram is said to be applied to a straight line , when it
is described upon it as one of its sides . Ex . gr . the pa• rallelogram AC is said ...
Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
added alſo altitude angle ABC angle BAC baſe becauſe Book caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides figure firſt folid angle fore four fourth given angle given in poſition given magnitude given ratio given ſtraight line greater half join leſs likewiſe magnitude manner meet multiple muſt oppoſite parallel parallelogram perpendicular plane produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained rectilineal remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 156 - 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.
Σελίδα 3 - 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.
Σελίδα 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.
Σελίδα 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.
Σελίδα 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.
Σελίδα 36 - 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.
Σελίδα 2 - 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 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Πληροφορίες βιβλιογραφίας
| Τίτλος | The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |
| Συγγραφέας | Robert Simson |
| Εκδότης | A. Foulis, 1781 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 466 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |