The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate1851 - 139 sider |
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Side 9
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
... demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ...
Side 10
... , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is therefore equal to the remaining 10 EUCLID'S ELEMENTS .
... , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is therefore equal to the remaining 10 EUCLID'S ELEMENTS .
Side 12
... demonstrated to be greater than it ; which is impossible . E But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the tri- angle ACD , the angles ECD ...
... demonstrated to be greater than it ; which is impossible . E But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the tri- angle ACD , the angles ECD ...
Side 18
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( Ax . 1. ) to one another ; therefore the angles CBE , E BD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ...
... demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( Ax . 1. ) to one another ; therefore the angles CBE , E BD are equal to the angles DBA , ABC ; but CBE , EBD are two right angles ...
Side 19
... demonstrated that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . If two straight lines cut one another ...
... demonstrated that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . If two straight lines cut one another ...
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Vanlige uttrykk og setninger
A B C ABCD adjacent angles angle ABC angle ACB angle BAC angle equal angles BGH base BC BC is equal bisect centre circle ABC circumference diameter divided double draw a straight equal angles equal circles equal straight lines equal to FB exterior angle given point given rectilineal angle given straight line gnomon greater half a right hypotenuse interior and opposite isosceles triangle less Let ABC Let the straight line be drawn opposite angles parallel parallelogram perpendicular PROB produced Q. E. D. PROP rectangle AE rectangle contained rectilineal figure remaining angle right angles segment semicircle side BC square of AC straight line AB straight line AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle