In 1603, german astronomer christoph scheiner began to copy and scale diagrams using an instrument that came to be known as the pantograph. by moving a pencil attached to a linkage, scheiner was able to produce a second image that was enlarged. do some brief research on scheiner’s invention. describe how the pantograph works and how it is able to produce an enlarged image. how does the operation of the pantograph relate to dilations and similarity? how can you use similar triangles to describe why the pantograph works as it does? write an abbreviated paragraph proof using similar triangles to explain the design. in many instances, the pantograph has been replaced by other means for enlarging images. what has the pantograph been replaced by? explain. 13 response(s)

1.    The pin’s location aids to create two drawings simultaneously. This is that while drawing an image, a copy, which may vary in size, is created at the same time.

2.    The pantograph relates to dilation and similarity due to the use of similar triangles that affect the scale of the second drawing.  

3.    The use of similar triangles illustrates the process of the pantograph because the ratio of similitude is set when determining where to place the pin. When a triangle is moved while tracing a line, along with the outline of the image, an enlarged/reduced version of the image is created by the other pantograph's end.

4.    The pantograph is now obsolete and has been replaced by several different ways of producing duplicates such as photocopying, mass printing, and digital filing.

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

step-by-step explanation: