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Defining the demand for central bank money as $ [c + \theta (1-c)]M^d $, where c = percentage of money people keep as currency, and $\theta$ the reserve rateo, I don't understand why, as my book states, an increase in either c or $\theta$ would result in a right shift of the curve.
My reasoning is: $ [c + \theta (1-c)]$ get's higher and $ M^d $ is a negative sloped function, therefore $M^D$ should get steeper.
Well this depends on parameters of $M^d$, but for reasonable parameters $M^d$ always shifts to the right. I assume your textbook uses linear money demand for example $M^d = c - b i$ and so on.
Denote $[c+θ(1−c)] = \gamma$, then for linear downward sloping demand we have:
$\gamma M^d = \gamma c - \gamma bi$
if $\gamma$ increases demand shifts to the right for any parameters save $c=0$ or $\gamma=0$ (assuming all parameters have to be non-negative). Demand will also become steeper as long as $b >0$ but you will always
